I don’t know where you got that idea. There absolutely are those peoples still living in Essos, just changed somewhat due to 400 years of history going by. So if we go looking for the Andals, we find them in Pentos:

“Pentos is the nearest of the Free Cities to King’s Landing, and trading ships pass back and forth between the two cities on an almost daily basis. Founded by Valyrians as a trading outpost, Pentos soon absorbed the hinterlands surrounding it, from the Velvet Hills and the Little Rhoyne to the sea, including almost the whole of the ancient realm of Andalos, the original homeland of the Andals. The first Pentoshi were merchants, traders, seafarers, and farmers, with few of high birth amongst them; perhaps for this reason, they were less protective of their Valyrian blood and more willing to breed with the original inhabitants of the lands they ruled. As a consequence there is considerable Andal blood amongst the men of Pentos, making them perhaps our closest cousins.”

They just intermarried with the Valyrian colonists. But they’re still there, living in the same hill country that Hugor of the Hill did. 

Likewise, if we’re looking for Rhoynar, we can find them on the Summer Isles, on Abulu the Island of Women, where “A few thousand of [Nymeria’s] followers
chose to remain behind, however, and their descendants remain on the Isle of Women to this day.” We can find them on the Stepstones, where “even now there are isolated pockets of Rhoynar on the Stepstones, claiming descent from those who were shipwrecked.” And more unhappily, we can no doubt find them in chains in the Volantene empire, tilling their ancestral fields to benefit the Old Blood. 

If we’re looking for Valyrians, we have of course “eight of the Nine Free Cities are proud daughters of Valyria that was, still ruled by the descendants
of the original colonists who established themselves there hundreds or thousands of years ago. In these cities, Valyrian blood is still greatly prized.” Now, over 400 years, there’s going to be some change, and there’s a good deal of variation. So in Lys, they say that “here more than anywhere else in the known world the old Valyrian bloodlines still run strong…The blood of Valyria still runs strong in Lys, where even the smallfolk oft boast pale skin, silver-gold hair, and the purple, lilac, and pale blue eyes of the dragonlords of old. The Lysene nobility values purity of blood above all” whereas the Myrish interbred with another people: “Myrmen are believed by certain maesters to be akin to the Rhoynar, as many of them share the same olive skin and dark hair as the river people, but this supposed link is likely spurious. There are certain signs that a city stood where Myr now stands even during the Dawn Age and the Long Night, raised by some ancient, vanished people.” And of course, in Old Volantis, you have the Old Blood of the city who dwell within the Black Walls, such that “many Volantenes regard themselves as the natural and rightful successors to the dragonlords of old Valyria.”

And then at last you have Braavos, which from the beginning was a melting pot of every possible ethnicity in Essos:

“Since the escaped slaves came from many lands and held many faiths, the founders of Braavos created a place where all gods were given their due and decreed that none would ever be made paramount over another. They were a diverse people, whose numbers included Andals, Summer Islanders, Ghiscari, Naathi, Rhoynar, Ibbenese, Sarnori, even debtors and criminals of pure Valyrian blood.”

So there you have it.