Does it make economic sense for only some universities in a certain area to pay their sports scholars?
I mean, even in the US, the ability of a school to offer sports scholarships is determined by what athletic conference(/division) they belong to: Division III schools are forbidden from offering athletic scholarships. (So in that regard- it can vary even at the city level. Boston has some schools that give athletic scholarships, and some that don't). In fact, in that example, Northeastern University provides athletic scholarships, but three blocks away is Wentworth Institute of Technology that doesn't.

As far as why would someone play a sport without the possibility of scholarship? For some, I'm sure it's the potential for a future athletic scholarship (for example, many US football players will play their first couple of seasons for a community college in the hopes of attracting attention from NCAA Division I programs). For others, I'd guess the potential of going pro- if you didn't get offered a spot on a team that provides athletic scholarships, this might be your only chance to improve and try out for a pro team later.

But for most, I'd guess it's probably because they enjoy it. Many US schools have club teams in many sports, which compete against local schools and offer no real chance for financial returns. Moreover, why do so many students participate in other competitive extra curricular activities? I'd guess the same reason.