Are there areas where only some universities pay their sports scholars? I have a feeling this is off-topic because this is about undergrad and not about research, but this question Why do American colleges and universities have sports teams? isn't closed, so yeah here goes.
Apparently

‘Athletic scholarships are common in the United States, but in many countries they are rare or non-existent.’

But are there countries where there are some universities that offer sports scholarships while other universities in the same country don't? We can shrink country to city, town, district, etc if you like (Note 2). I'll just say 'area'.
I have this relative: My relative and I are expats living in a certain area but permanent residents of the area. My relative recently got accepted into a first world university for an undergraduate degree in engineering and was accepted as a sports scholar...sort of.
None of the tuition is waived. The only thing my relative gets is a reduced fee to be on the team: Yeah, the university charges its students a fee to be on the team. My relative also gets lower grade requirements in admissions or retention, but my relative does not need that due to having outstanding grades in secondary. I figured this was a practice in this area where we both live and where we are both expats (see quote above).
However, I found out that several universities in this area apparently do offer sports scholarships ranging from 50-100% off tuition. One of the universities that offer is even of a lower QS ranking than the university that my relative is attending (Note 1). This to me seems like a big misunderstanding on my part, so I've emailed the university, although my relative has already asked, just to get first hand confirmation.
In the mean time: Why would anyone play sports for a university against other universities but not get paid or get tuition waived for the playing?
Some guesses:

Lower admission grade requirement
Lower retention grade requirement
Admission or retention for dormitory requirement
Possibility of future scholarships
Prospects of a sports-related careers after graduation that include but are not limited to professional sports

The thing is none of my guesses explain why those universities apparently have sports scholarships that waive tuition at least partly while this university doesn’t. Why wouldn’t sports scholars from a university that doesn't pay their sports scholars just transfer to another university in the next year thus causing the university to lose in inter-school competitions?
(Note 1): My relative applied to all universities in our area for sports scholarships and was rejected for all but this university. Also, our area has less than 10 universities, and they're all in the QS... Wait, lemme check...Yeah, ACTUALLY, my relative's university has the highest world QS ranking in our area. Meanwhile, the university with the lowest world QS ranking in our area has sports scholarships. Also, all universities in question are in the top 100 in our continent's world QS ranking, our continent is not Africa, and my relative's university is not the highest in our area for our continent's world QS ranking.
(Note 2): I'm thinking perhaps of a possibility where, say, in North America or Europe this might be the case but is not the case for a specific state or city or something like Massachusetts, Boston, UK or London. You can shrink as much as you want on the condition that universities in your shrunken area compete with each other in sports.
Update 1: Relative is sibling. saying this just to link to posts. lol.
Update 2: Starting 2nd year of university, sibling got into dormitory scholarship. So, tuition scholarship isn't the only thing student athletes can get. (Sibling is now 3rd year going 4th year.)
In the United States, many (perhaps even most) institutions do not give sports scholarships. 

For example, I went to MIT, which gives only need-based funding (0% sports scholarships), but has a quite high NCAA varsity participation rate because, well, sports originally exist because people enjoy playing them, especially in the company of others. That's certainly why I was a student athlete (even captain of my team). 

What institutions without sports scholarships tend to lack is not athletes but audiences.  At MIT, for example, the varsity football games were infamously said to be better attended by the band (who loved chances to play) than by anybody else, though I can't verify this because I never bothered to go myself.

By contrast, the institutions that do give sports scholarships tend to have big crowds and be the high-visibility teams that you see on TV, thus exaggerating their apparent frequency.

Given the wide mix of public and private institutions with varying philosophies and missions, I expect you'd likely find this contrast in every major US city.