I understand the purpose of an ante: it stops people from constantly folding until they get perfect cards. But what's the point of having different players bet different forced bet amounts? It just seems "unfair" without adding anything to the gameplay.
There is nothing "unfair" when it comes to the blinds, because the blinds "go over" all the players at the table in a Round Robin method.
The blinds have some purposes, the most important of which are:
EDIT: this part is added as a response to your comment.
Ante is a very aggressive way of force players to commit chips. ANTE is as used as long as the tournaments continues. usually, an ante is not used in cash games. To make things a little bit clearer - there are some games (like 7 stud, 7 stud hi-low, razz ) that ANTE is part of the initial payments.
regarding the third point: players perform sometimes unexpected moves like big raises or All-in. those moves are sometimes used as a tool to cause all other players to fold their hands. By doing so, they earn the pot.
regarding the forth point - buy-in is usually for tournaments. For cash game we have the size of the blinds to tell us if we can afford ourselves to participate in the table.
The sole purpose of antes and blinds is to give every hand equity.
That is short and curt, but consider if a poker game has no ante or blind no hand has any real expectation. Without consideration of anything but optimal play what would be the optimal strategy in a game without blinds or antes? What hand would motivate one to put any money at risk in a pot unless there was already equity in the pot? Poker is not a card game, it is a betting game, and cards are simply the most popular way we play poker. Blinds and antes define the scope of the betting. Technically, no matter what the medium, you don't have a poker game until you have a pot, blinds and antes are the start of the pot making whatever you do afterwards, poker.