Reality is the American casual viewers cannot relate to k-1 kickboxing. Most of them are just plain not good at it, so they don't watch it. Similar to soccer, most Americans are not good at that (on the elite world level) so they choose to watch sports that are more familiar to them like baseball, American football, wrestling. These sports are engrain in their upbringing (wrestling, football, baseball) as youths in schools. Most youth males wrestled and if not, think they can box (because that's all they are good at, its easy to throw a haymaker then to throw a balanced kick in a bar fight).
In MMA, particularly UFC, the rule set favors the wrestler (no spike elbows, no kick/knee to the face on the ground, lay and pray to win). Most casual viewers are able to relate to this style because wrestling and boxing is American, similar to American Football and baseball. So kickboxing/muaythai never caught on in the American main stream because plain and simple most Americans are not good at kickboxing, but most Americans can relate to wrestle+throwing a punch so MMA/UFC caught on quick. Typical, bar chugging bum would think he is a mma fighter, than an elite kickboxer any day because he will be unable to perform the skills of an kickboxer. Easier to grab and throw punches, so casual viewer can relate to this more and buy more pay per views.