The answer is an unequivocal feck no. Ole Gunnar Solskjaer is a serial loser and out of his depth to paraphrase a Scottish pundit.
I'll start by saying that it's bizarre for fans to demand world class defenders, midfielders and attackers but somehow be content with a mediocre Norwegian coach whose main qualification for the job is being a former player.
Myth: Give him time, even SAF and Klopp took a while to get it right.
Reality: Both SAF and Klopp had winning CV's and pedigree in spades. Ole has none of the pedigree required to manage the biggest club in the land.
Fergie won three league titles in Scotland with a team not named Celtic or Rangers, won a European cup winners cup against Real Madrid and a European supercup. Yes he didn't win right away at United, but he earned himself time. Klopp broke the Bayern hegemony in Germany, won 2 Bundesliga's on the bounce and a Pokal, drove his team to the CL final with some heavy metal football.
What does Ole stand for? What are the patterns of play he's iinstilling in the team. Expecting Ole to get it right at the highest level it's like expecting McFred to become Xaviesta if you give them time: it ain't going to happen.
Myth: All this chopping and changing is bad for the club
Reality: Not necessarily. Big clubs chop and change all the time. Chelsea has gone to 3 CL finals, and every single time it's been with a manager that did not start the season (Grant, Di Matteo, Tuchel). Bayern Munich won last year after geting rid of a mediocre Kovac. They changed coach again (in fact 7 or 8 clubs are starting with new managers in Germany and 6 or 7 in Italy) and I suspect they'll be super competitive again.
We've been sold this massive industrial scale overhaul that OGS is undertaking to turn around Manchester United, and on a longer timeframe than the Chinese take to build a megacity for million of inhabitants. I know English people are married to tradition and move slow, but it's a football club ffs, don't overcomplicate it. Get the right coach and the right players and 9 times out of 10 it will work jus fine. Sometimes you don't even need 5 years for it to happen.
Myth: We're definitely moving forward, there is clear progress.
Progress from what? We've gotten 66 points, 66 points and 74 points with Ole in charge. 74 points wouldn't get you a top 4 in a season when all the big 6 are having a good season.
2nd place is not progress when Liverpool, Arsenal, Spurs and Chelsea had an off year. Tuchel came in when they were 9th and they made top 4 and won the CL... that's progress. I expect United to fight for Top 4 next season, not titles unfortunaely. Which suits Glazers fine btw.
Myth: But the transfer spending at least has been good. AWB, Maguire, Van de Beek, Amad, Telles, Dan James, Fernandes have all been great.
Reality: It's a mixed bag. Ole didn't trust the bench against a second rate Spanish team in a European final. Between Amad, Dan James, Telles, Van de Beek he didn't have it in him to bring them before the 116th minue when the starting 11 were running on fumes. Individually Maguire and AWB are good players, but is our defense fixed? I would not think so. Why spunk on Van Der Beek when the priority is a CDM?
It's not all doom and gloom obviously. He's a good influence on the dressing room, he stabilized the club, he stands for United values of youth, he's overssen the emergence of Greenwood, the resurgence of Shaw, the transfer of Bruno Fernandes and Cavani. He's a United legend, and I'd rather win with him rather than another coach. But I'd rather win first. With Ole, I'm not sure we will. So I wouldn't extend, pure and simple.
Firstly, Ole is building a young team that is attack-minded and borrows from the principles of Klopp particularly. He wants to play a proactive, high impact and high energy pressing football. He wants us to build up our play out from the back, with a mobile double pivot who have the energy to go box to box, or a single pivot in the smaller games, wth a fluid attack further up the field who can score a variety of different types of goals.
Clubs like Chelsea, Bayern and Madrid can chop and change their managers because they actually have owners and a sporting department who are actually in it for the glory and success of the team. We have neither (this really shouldn't be up for debate and I'm surprised it's taken you in considering your anti-Glazer stance). We don't even want to spend the miniscule amounts required to make our women's team good FFS.
The asinine arguments over progress is hilarious to me. If you can't see it then that's a you problem. Since Ole has come in, he's been comfortably the best of the rest behind Pep and Klopp, from a situation where we were close to being cut adrift when he joined. That is progress. The underlying numbers also back up this progress. Has it been perfect? Absolutely not, but the circumstances he's in haven't been perfect either. He handled a pandemic a damn sight better than Klopp did. He also didn't have the transfer window that Lampard did, and the only first team starter he did sign last year was on deadline day a month after the season began and who couldn't even get on the pitch until a couple of weeks after that. He needs to do more, but also, the club needs to do more for him. Last summer's transfer window had all the potential hallmarks of the 2018 one where Jose melted down and we capitulated into midtable by December, but it didn't because Ole actually handled that period expertly and took the bumps. Considering also that he has built this squad up and regenerated it off the scraps and leftovers left behind by Jose (the only bonafide starter that both Jose and Ole have in common now is Lindelof, and up until this season you could have added DDG - that's it. Just two out of 11 who both Jose and Ole wanted to play regularly) and that he's only made 4 first team signings in the two years he's had, I think he's done enough to deserve that new contract, irrespective of what you feel someone else could have done.
The players he's signed have predominantly been long-term in nature, so to say that they've been a mixed bag is short-termist and a bit obtuse to say the least. James wasn't signed as anything but squad cover. Telles did what he was supposed to do and that was to drive up the standards of Shaw. VdB is a longer term signing who was bought to replace Pogba in the event he left (which seemed to be very much on the cards at the time), but that is now looking unlikely, so we'll see what happens there. He needs to improve in his trust of the squad but likewise the squad have to earn that trust. People like you seem to ignore that Ole was actually being criticised for using his squad too much earlier this season just gone, and was told he was unnecessarily tinkering with the lineup and formations (e.g. after the Leipzig game in particular). He got the balance right on that front after that game but then the Sheffield United home game happened (where Telles, Matic, and Axel all started) and the squad players but particularly those guys, lost their trust. The villareal game was a one off where he played all his best players at the same time. Usually greenwood would have been on the bench and likely would have come on if the game situation demanded a change but the likes of Amad are too young to be thrust into a situation where penalties could potentially occur, and VdB would have been as useful as a marzipan dildo in such a situation as he doesn't provide the cutting edge. Mata, as we all know, doesn't have it in him anymore. And who else was there, Matic? Nuff sed.
So, like I said, for every argument you've raised, there's a counter. I'll repeat, Ole isn't and hasn't been perfect, but the circumstances he's in haven't been perfect either but better managers than Ole have struggled this past season, yet he's one of the very few who has kept his club in a decent position almost all the way through the season. I understand the disappointment over the EL final. I was too, and if I'm honest, that game was the lowest I've felt as a Utd fan during Ole's tenure. But that's the thing about football, it has the potential to create situations like Wednesday. Steaua Bucharest beat Barca in the European Cup final in the 80s, relegation-doomed Wigan beat City in the FA Cup final more recently, and even more recently than that, they beat Pep's City side in Cup when they were in the championship/league 1.
At the end of the day, one bad day or bad game does not negate the real progress that's been made and with the age profile of this squad that Ole is building, it's only trending upwards rather than down. Add in a few first teamers in the 3-4 big holes that are in the squad, as well as fortifying it further with the very promising kids that are coming through, and you'll see a proper Utd team emerge, I'm sure of that.
All in all, Ole will still be here next season and probably will get a new contract, and deservedly so. No amount of flagellation, entitled whining or complaints will change that, so why don't you just get behind the team? If your dislike of the manager is so strong, then perhaps it might be best for you to find another hobby? Cos football and Utd obviously don't seem to be doing it for you...