> And more importantly, FPTP doesn't allow for middle ground. If you are in the middle, you can't get elected, because neither party would nominate you.
Median voter theorem claims a mathematical proof of the opposite, that FPTP has both camps having a dominant strategy of appeal to the median voter. Both your assertion and median voter theorem fail in practice; the latter because it ignores issues of salience, distribution of views (unimodal vs. multimodal), turnout and mobilization effects, etc., and yours because, well, it ignores much of the same things, but assumes different generalities about them consistently hold.
> If we had a electoral system that tended to elect the first choice of the median voter, things would be dramatically different.
Actually, the vast majority of US voters, even those that self-identity as independents, are highly partisan — the median voter is probably a reasonably strong partisan of whatever party has the current turnout advantage, which is essentially what FPTP elects.