Kane being just a finisher is straight up wrong though. I don't mean to be offensive when I say this, but genuinely have you watched him this season? I feel like nobody who watches Kane consistently could possibly see him as an Inzaghi type player. If anything, he often drops too deep these days in an effort to see more of the ball. His ability to hold up the ball and bring our wide players in to the game are some of his strongest assets, some of his passing this season and last has been absolutely glorious. He is absolutely the complete striker, and this isn't just Spurs fans who are saying this, it's mostly everyone (In particular ex-strikers) who basically regard him as easily one of the best in the world, and far from a limited poacher. He's turned in to an incredibly well rounded player under Pochettino, and a lot of that is owed to his fantastic attitude and work rate.
Martial has a long, long way to go before he should be even mentioned in the same sentence as Kane. You're talking about a guy who has been crowned top scorer twice in the league, scored 41 goals in all competitions last season, has banged in 16 goals in the champions league, won the world cup golden boot and is currently the top scorer in the league with 14 goals and 4 assists, well on course to hit 40+ in all comps once again. Martial didn't even make the French squad and has spent the last couple of seasons drifting in and out of the United team, now you can blame Jose for this but that's the reality of his situation. There's simply no logical comparison between the two players, Kane is miles ahead unless you're going by some vague, subjective notion of who has more 'talent'. A few good games against relegation fodder and Martial could be ahead of arguably the best striker in the world in 'no time' ? Honestly.
You're obviously entitled to view Martial as having fantastic potential, but outside Manchester United are there any fans who think Martial could easily overtake him? It's not just fans from Spurs who would find that pretty dismissive of what Kane has achieved and the level he's playing at. There's only a select few in the world right now who are ahead of him at all, let alone easily. I think it's a classic case of Kane being underrated because he's not a particularly flashy or showy player, so therefore he's not perceived as all that talented. The fact is he's one of the most natural finishers in the world with movement off the ball Martial could only dream about, among other assets. Like you say Martial can do more 'with and without the ball' and what do you mean by this exactly? Without the ball Kane is miles ahead of Martial, his movement in the box is some of the best in the world, it's part of how he's so ludicrously consistent at scoring goals.
Sorry, this turned in to a bit of a rant. I just find it weird that Kane still gets underappreciated by some. I mean, what more does a player have to do as an individual? I suppose some will say win trophies, but I don't think it would be remotely fair to say any of our failings are down to him. The rest of your post is totally fair and I agree with, there's no way you need to bring in somebody like Eriksen when you have a talent like Pogba in midfield, and it's good to see Rashford doing well as an England supporter. I agree that going forward Lingard is probably a weaker link, but even then his movement off the ball is fantastic and he has a great attitude, so it's hardly a huge weakness.