62/65 (95.4%) of P5 schools are Tier 1 Research Universities*
62/83 (75%) of Tier 1 Research Universities with a D1 football program are in the P5**

If you're a Tier 1 Research University and not a P5, it's more likely because you don't play football (23 schools) than it is that you're stuck at G5 wanting an invite (21).

It's clearly not the only thing and it can certainly function as an excuse, but there's definitely a strong relationship. My argument is that if there's a strong correlation and we want to increase our academic reputation anyway, we should be making moves to take it off the table as an excuse.

*P5 schools that aren't Tier 1: Baylor, TCU, Wake Forest

**Tier 1 schools in G5: Colo St, Florida International (since 2002), Georgia State (since 2010), Rice, Temple, Tulane, Buffalo (since 1999), Alabama-Birmingham (UAB) (since 2017), UCF (since 1996), Cincy (since 2013), UConn (since 2013), Hawaii, Houston, UMass (since 2013), UNLV, Nevada-Reno, New Mexico, North Texas (since 1995), South Florida (since 2013), Southern Miss (since 1996), UTEP

You might also note that the majority of those programs haven't been G5 for long, either because they're a relatively new program or because they previously were in a BCS conference (Big East)