Like most things, both of your are off. If you're making a game to play at a convention or game store and there are lots of players, you can take the above view and just axe a player who refuses to accept the concept. However, a lot of us play with friends.
I've bee playing with my current group for a long time. The newest player, the son of the guy I've been gaming with since 1984, joined us 16 years ago. Kicking someone out of the game because a no magic campaign isn't something he would enjoy isn't an option.
If a player came to me wanting to be the last wizard mentioned in
@pemerton's post, I'd either scrap the campaign and find something everyone would enjoy, or I would try and come up with a compromise. Perhaps he would be okay playing an eldritch knight or a wizard to a max of 4th level and then multiclass. Then it could be a really low magic campaign and he would have some magic to play.
Going straight to, "Kick the player out and find someone else" will often not be the best answer,