FFXIV has certainly taken a different route as far as "origin" cities are concerned. They're no longer pegged to our characters' race, but rather to their starting class. That's likely to be a deliberate attempt to make players look past race, and build a world that's based more on ideology than ethnic nationalism.

For me, the three city-states represent the values of pragmatism (Limsa Lominsa), profit (Ul'dah) and preservation (Gridania). And all the classes and disciplines associated with each city ultimately revolve around those themes.

In short, it really doesn't matter which city is the "more likely" origin city, based on race. But I can see where the OP is coming from, as I had asked a similar question some time back, about which parts of Hydaelyn the races originally came from, to get an idea of where in Eorzea you're more likely to find them.

Incidentally, the way I rationalise the sheer number of miqo'te adventurers all over the realm is simply to imagine that the catfolk, being relatively recent arrivals to Eorzea, still retain their independent, nomadic habits. Hence their proclivity towards adventuring. To some extent, the same can be said of the hyur. The reason you won't see quite as many elezen and roegadyn is that these folk have largely settled into sedentary professions, and are less likely therefore to be roaming the realm.