Bezalel: Yes, but we don’t know what kind of peyos they had, now do we?
OP: I think your original premise (Teymani Jews were undisturbed by outside influences) is highly questionable, if not plainly incorrect. First, the whole of the Arabian Peninsula has been populated since ancient times, both by nomadic tribes and smaller settled communities and city-states. Second, Yemen, of all places, was probably more susceptible to external influences than many other places in the Peninsula; it sits at the juncture of some of the most important sea-trade routes in history. The trade between China, India, Indonesia, East Africa, Egypt, and the entire Mediterranean Basin passed along the Yemenite Arabian Sea and Red Sea coasts.
Even if you are correct that Teymani Jews practice Judaism as closely as possible to the original B’nei Yisrael, I’m not sure why this should matter. Teymani Jews live in a culture most akin to that in which the original B’nei Yisrael lived, so it makes sense that their customs would be similar. For the rest of us, it seems that we follow the customs that have developed out of our own unique individual, familial, and communal experiences throughout the world. Our customs are preferable for us precisely because we do have interactions with other cultures, and our customs grew out of those interactions. Teymani customs are not halachah. As another poster pointed out, they are not recorded in the gemarah; they are not particularly preferable or halachik, otherwise they would have been recorded for posterity by the compilers of the Torah shebaal pe.
Teymani customs are preferable for Teymanim (again, if your original premise is correct) precisely because Teymanim were isolated and there customs grew out of their unique circumstances. Our own customs are preferable for us precisely because they grew out of our interactions with other peoples and represent the way we molded the non-halachik aspects of our practice to deal with our particular living conditions.