For starters, the statement that winning a G5 gives access is false. It guarantees nothing. How many G5 champions outside of the top 12 got a NY6 bowl invites. Of those teams, how many were undefeated or one loss.
It may be easier to have a great record in a G5 conference than independent. That point I will concede. Which is a good argument for joining the Sun Belt.
Joining a G5 is a step backwards and recruits will take notice of that more than anything else.