It's because we have open primaries in the US - registering as a Democrat or Republican is only important as far as voting in primaries. In other countries the selection of candidates is internal to the political parties themselves. There are pros and cons for both systems but the US system is fairly unique globally aside from a few exceptions in South America.
Isn't it kinda internal here too? Parties get to pick their candidates how ever they want. The major ones have primaries, but I still don't know if anything legally requires them to respect the votes there.