Part of the LP is set on winning elections. I'm not joking. While a very, VERY distant third, there are some LP elected officials, and they want there to be more. That puts some severe limits on what your positions can be. It's hard enough to get elected just without a R or a D next to your name. Much less being actually controversial. There's a wing that wants to be as unthreatening as possible to sort of sneak into political power through the backdoor.

Most other 3rd parties, with the possible exception of the Greens, are more interested in advocacy and making political points, with the full knowledge that they're not going to win.

Truth is it hasn't always been Republicans and Democrats in American history, though there has rarely been more than 2 major parties. More likely, I think, than a 3rd party rising to prominence is either the Rs or the Ds balkanizing along ideological lines, with one faction eventually winning and the other disappearing. The electoral system virtually guarantees that there will be 2, whatever they are called.