They're not really centerists, they're just trying to stir the pot. Jon Stewart had a really good podcast on all this on the Weekly Show. I could only find a youtube video on my laptop, I think it's the full thing by the time.
None of what you said is how anything works in US government. Biden has some crazy takes on the war in Gaza, but it's rooted in them being our allies and something else that I have no idea about.
3rd party in a 2 party system just takes away votes from another person. You have to calculate who that's gong to be and assess the risk to the people and government.
When a single party is in charge of the both the house and senate and there are no assholes that can be bought off, that's the only time things can be changed.
Then it's confirmed that I don't agree with you that that's what is happening with the Biden administration. They're trying to keep our allies from being bombed originally and now they're tied up in a shit dumpster.