big if, one that I'd wager most of them do not succeed at.

Sure, but the opportunity is there.

And while its equally true for regular athletes, those guys also are still peak physical specimens

While they're working out, yes. Tons of former athletes just become fat and out of shape, though.

who are probably at least somewhat capable of being social.

Quite possibly, but not always. "Uhhhhhh, obviously they're a great team, uhhhhhhh, at the end of the day uhhhhhh we have to play harder to get the W" is not exactly peak charisma.

Also, this assumes they haven't been injured during their career -- which could reduce both their charisma and physical fitness. Family Guy did a funny bit about this.