Not only that, but FPTP mathematically will always pull the two parties to the center, a hair's breadth apart from one another, because anyone who wanders off into "their" territory will start to lose elections because of it.

I mean... well, that's how it works mathematically. It's not even really applicable to modern US politics. What's happening in modern US politics is that:

1. The voters are so addled by propaganda that they can't even really tell what's going on, and mostly make decisions based on pure engineered fantasy instead of based on anything that's actually happening ("Immigration is a problem! Trump is going to fix that problem!" and similar beliefs)
2. Even through the fog of propaganda, there are some things that they're able to figure out (health insurance companies are a massive problem and we shouldn't let billionaires keep all of our work output while we're struggling to pay rent and buy eggs). But, the people in Washington by and large don't support fixing any of those things, because the people who pay their bills don't agree with the obvious solutions that 85% of the people would support.
3. Party machinery and media monopolization (and now, social media propaganda) prevent anyone who's invested in those popular things -- the "center" that FPTP math would normally be pulling the politicians towards -- from gaining any traction or being able to put anything better than a cruel caricature of it into practice (see also the ACA).

Basically, we fucked. But, if we someone managed to unfuck those massive problems, then we'd still be faced with FPTP pulling everyone to "the center." But, on the other hand, "the center" would be way better than the current American system of one conservative party running against one openly fascist party and like 5-10 rabble-rousers on the left running around Washington and making noise about how really in a perfect world it shouldn't be like that.