The problem is first-past-the-post always leads to strategic voting, which leads to eliminating 3rd parties. And, once you have only 2 viable parties, they benefit immensely from FPTP, so they're unlikely to ever get rid of it.

Unfortunately, game theory was invented in the 1940s, and the USA was invented in the 1770s, so the founding fathers couldn't make use of game theory to work out a good electoral system. Oh, and having to compromise with the slave-holding states and devising an electoral system that gave them power turns out to have had bad effects down the line. Who knew!?