If we play in this style for ~80% of our remaining matches (winning at least 70%-80% of the matches), players look improved, we score more goals and generally it looks like a happy camp, I'd give him the job in a heartbeat. I rate Pochettino and Zidane very highly but there's literally no point in getting them if Solskjaer does what I previously stated. Having a connection to the club is always a plus.
As said, a DoF is needed to take the transfer responsibility off the manager anyway.
People might see some hypocrisy to this with the reluctance for supporters to back Giggs taking the job but to me, that was more about the 'risk' of appointing him at that time. Ole has come in at a time when we could afford to take that risk. Secondly Giggs is a wet blanket and his personal life issue was disgusting (so it's hard to back him 100%). But of course if Giggs had come in and got us playing good football and got positive results, we'd obviously want to keep him over getting Pochettino/Zidane/Tuchel whoever as well.
If Ole doesn't keep up these performances, that's fair enough. The club needs to plan for all scenarios. I just think the idea he couldn't be in the running is insane.