No, it doesn't.
> If a party gets much more extreme than the populace then they will lose easily against an opponent just a little more moderate than them.
This requires lots of assumptions that may not be true in the real world. First, it assumes a party in power can't shift the electorate by suppressing voting rights of its opponents. Second, it either ignores propensity to vote effects, or assumes a unimodal distribution of preferences so that moderation not only brings you closer to the median voter but also doesn't make people who are closer to your position less likely to vote; whereas a two-party system over time promotes a bimodal distribution where moving away from one of those peaks, even toward the center between them, reduces enthusiasm and votes recieved.) It also ignores communication assymetries and their relation to money, and therefore support from moneyed interests.
It might result in more centrist parties (though I've never seen a convincing comparativr argument or evidence; median voter theorem is fine and all for the abstract idealized world it applies to but ignores pretty much every significant aspect of real-world political dynamics), but even so it doesn't seem to lead to more centrist governments.
> I honestly think that multi-party systems might be better but I also think that two party systems aren't completely aweful
Among democracies, degree of proportionality of representation is pretty directly correlated with popular satisfaction with government, and smaller numbers of parties are correlated with poorer proportionality; from the perspective of providing people the government they want, two-party systems turn out to mostly be, empirically, pretty awful, and the US's particular implementation near the bottom of the barrel among established democracies.
While dual or multiple parties can affect this, the degree of representation currently in the US is currently more of detriment to finding a middle ground.
The average member of the lower house has around 650K constituents more then any senator did at our founding. The US Constitution was suppose to allow the House to grow and expand as the country did, however Congress passes a law setting the limit of members to the House almost a century ago.
If we multiply the House by 10, each member represents 65K we are still within the Constitution and will get closer to what you are stating then a complete overhaul. This has the effect of give more representation to people and makes it more likely to get to a middle ground. As an example a district votes 60% for one party in the current system results in 40% being unheard. With a 10x, keeping in mind it wouldn't really work entirely we have, 6 members that agree with the 60% and 4 members that agree with the 40%. It's not going to be that exact but hopefully you get the idea. This is going to decrease the power of each member of the lower house to state "Mandate" and force getting closer to middle ground.
In the 60/40 example it is mostly likely gerrymandered or a state with a single member in the House which results in no general election. The district is already assumed to win the general and thus the primary becomes the real election which is nominally 50% of the a general election. So in the current system 30% of the 650K in our example district effectively elect the member to House. Given typical 50% voter turnout we then can say that basically say that about 15% of of a district pick the representation. So in our example 98K are represented fully and 552K people are under represented. By scaling that back we would probably have less gerrymandered districts but even in this extreme we have 10K people vs 55K people and may even be able to increase voter turnout since a vote actually matters at this point. In my district my vote is worthless, I still vote in primary and general, but I live someplace more gerrymandered than the 60/40 it's closer to 80/20.