OK. You know it isn't enough for me to just compile some numbers, so I made a chart to give us a visual representation. Make of it what you will:
I've looked this up before, but it is noteworthy how close the AO, RG, and USO are in terms of number of winners: 27 each for AO and RG, 29 for USO. Wimbledon has significantly less, with 21 (this is Open Era only).
Each has their own "shape" that tells a different story: Obviously Rafa's 14 RG titles. USO stands out for not having any player win more than five, and also more (6) with at least four. Wimbledon has a "Big Three" (four, if we account for Borg's short career). The AO has Novak doing a "semi-Rafa" and then more multi-Slam winners, with a lot of guys winning two.
As for the word "parity," when I hear that word in reference to sports I first think of the NFL and how they've used salary caps to bring team's closer together; that is, create greater competitive parity. In the NFL, just about any franchise can be good within a few years. Even the best franchise of the 21st century--the New England Patriots--"only" won 6 Super Bowls in a span of 18 years, and never more than two in a row. MLB has far worse parity, with maybe half of all teams never really being competitive except for maybe brief spans of time.
As far as tennis is concerned, I think of the way talent is pooled and how Slams are distributed. As we've discussed and is well known, during the Big Three era, there wasn't a lot of competitive parity: three players won not only the vast majority of Slams, but the vast majority of big titles. But this has always been the case in men's tennis: you have a small group of elites gobbling up most of the big tournaments, then a larger pool of second tier players winning the rest, with the occasional stray "third tier" player winning a Master's or even maybe a Slam. The main difference between the Big Three era and before is not only did they maintain their hegemony for longer, but it extended more fully into the non-Slam big titles.
@PhiEaglesfan712 can speak for themself, but I'm guessing what they mean is that the USO hasn't had a single dominant winner like the AO and RG, or a small group of players that stand significantly ahead of the pack like Wimbledon. But I'm not sure that this means there is greater parity, and I certainly don't see how this would give Roger any significant edge in the GOAT debate. Five USO titles in a row is very impressive, especially considering that it is evident that the USO has been harder to rack up big totals than other Slams, and probably for the reasons that Phi said (placement in the tour schedule). But...I don't see this as a significant indicator of GOATness. It is more of an anomaly due to a combination of Roger's early dominance and, as Kieran likes to say, the opportunity of the context in which he peaked.