You can't give non-athletic aid out to athletes with different rules than for non-athletes (yes, I realize that doesn't mean that schools don't bend/break the rules)

As for the "Flutie Effect," it's mostly bogus. From wiki:
"Writing in the Spring 2003 edition of the Boston College Magazine,[4] Bill McDonald, director of communications at Boston College’s Lynch School of Education determined that “Applications to BC did surge 16 percent in 1984 (from 12,414 to 14,398), and then another 12 percent (to 16,163) in 1985. But these jumps were not anomalous for BC, which in the previous decade had embarked on a program to build national enrollment using market research, a network of alumni volunteers, strategically allocated financial aid, and improvements to residence halls and academic facilities.” He also observed that “in 1997, one year after revelations about gambling resulted in a coach’s resignation, 13 student-athlete suspensions, an investigation by the NCAA, and hundreds of embarrassing media reports, applications for admission came in at 16,455, virtually unchanged from the previous year. Two years later, when applications jumped by a record 17 percent to 19,746, the surge followed a 4-7 year for football.” Going further back in history, he reported that applications had increased 9 percent in 1978, a year when BC football had its worst year ever, with a 0-11 record"

People like to point to the '99 and VT for the same kind of effect. Yes, there was a bump. But we were already on an upward trend. And a year or 2 later, we had returned right back to the already established trend. The notion that we've become a better academic institution because of football is far-fetched. Yes, it has some impact on awareness. Yes, it helps keep alums connected and donating. But we're a good academic institution because of--wait for it--academics. Crediting football is a slap in the face to the thousands of people who actually do the academic work.