Research aligns with academics (and is sometimes essentially the student's sole academic work in grad school). Sports does not align with academics, therefore we're talking about apples and oranges. Additionally, a student who is focusing on research will almost invariably be a PhD student and if they're one of the top students will surely have a stipend so it's not really a "scholarship" (nitpicky semantics). Some schools view them as employees/students.
There are definitely exceptions, but in 90% of the cases an undergraduate transfer is detrimental to the student's academic progress. For example, every state is different, but in NY we can only accept a certain % of a student's prior work towards their degree. This means that many students transferring in will have to retake courses, or even take additional ones to graduate.
Like I said, a graduate student is a different ball of wax. I actually view it as detrimenal to the student's academic careers if you forced them to pursue a graduate degree at their undergraduate institution.