I doubt the wizards at Hogwarts would be disinterested if a mf rolled up with a magic sword, freakish strength and speed, and an ability to quickly read their opponents' moves after seeing them once...
Ultimately the question is are Will's skills useful to the Tower, and he's shown many times over now that the answer is a resounding yes. If the world is at peril, why wouldn't you use any and all resources available to you? Prioritizing some cheap sense of pride and supremacy instead is ludicrous. Then again, Omori seems obsessed with constantly beating down on an underdog, so let's run it back for another ludicrous arc I guess...
Lucia's Malfoy or Voldemort or Slytherin (using the analogy), wouldn't care about that. All they would care about is their status as purebloods being threatened, and the fact some random muggle shows up.
They may not have the power to stop the other faction from letting him come to hogwarts, but they can have an influence on what privileges he can enjoy.
Using Will as a resource(a tool) has little to do with him entering the Tower. They could use him as a tool and not let him in the tower, in the same way a professor uses a plumber to take care of crap but doesn't let them attend the college as a student or give him an honorary doctorate.
Prioritizing pride and supremacy and keeping the power structure intact is literally something that happens all the time. It's not some bad writing by an author, but literally how reality normally/frequently works. Its politics. Bad writing is whoop, Will saved the city, so every person is delighted about it and instantly loves him. Including those who were doing whatever they could to keep him out of the Tower, guess they just change their minds and accept him as one of theiTower.
Bad writing is "hey the legal elimination of slavery arc is finished". Guess all former slave owners just accept slaves as completely equal in totality and never try anything to oppress those people again(No Jim crow/segregation/discrimination arc)
If the avengers were all early 1900s KKK members do you really think they would just let Sam Wilson, Black panther and Rhodey join them as full members? Sure, earth and perhaps the universe is under threat by villains, so they are forced to work with them and use their strength against their enemies. The enemy of my Enemy is a useful pawn. That doesn't mean they let them enter Avengers facilities, or go to the shwarma after party with them. That doesn't mean they don't haze those three.
Again, Will entering the Tower has nearly zilch to do with keeping humanity safe or not. He can be an asset used by the Tower and researched if neccesary, outside of the tower.
There are three main factions at play: those that support Will and support change to the Tower, those who are neutral to Will, and those that oppose Will and seek to preserve the status quo as much as possible.
Will has proven a valuable asset, and barely failed qualifying to enter the Tower using a technicality. So the faction opposed to Will entering the tower can't stop him entirely, and the faction supporting Will can't offer their full support.
Maybe the author will drag this on endlessly as you say. Or perhaps Will will successfully cement a position/place for himself in the towers power structure in events to come. Perhaps will being colorless is even the idea of the pro Will faction for that very reason, to change the tower.
All of this comes down to my basic point: Will encountering resistance after entering the Tower is not bad writing. Him encountering no resistance would be. Where things go from here, determines whether the author continues underdog arc continually, or whether the author pulls off good narrative development.