It still reduces mobility vs. just renting though. Now you're a landlord and probably dependent on the rental income to pay your rent in the other city/country. Obviously, it's all doable. But it's clearly a constraint (even if it's a worthwhile one) relative to not owning.
Not to mention that, at least in the US, most owned homes are single-family homes in the suburbs and the rental market for those is significantly different than a flat in the city.
