The problem with these conversations is most of us are talking past each other.
When you say P5 you seem to be referring to the prestige, aura, tingly feeling or whatever that comes along with watching Alabama play Notre Dame in front of 100k fans. And you are right in saying that Houston and Memphis will never replicate that tingly feeling no matter how many NY6 bowls they both go to.
My issue with that definition of P5 is twofold: first, there are about 70% of P5 teams that have more in common with the G5 than they do with Alabama, if we are going on aura, prestige, money etc.
And second: BYU is closer to Alabama in prestige, success, and fan support than we are to Wake Forest and Purdue. And yet they are P5s and we are not.
The most concise, universal definition of P5 status is belonging to a conference whose champion automatically gains access to the NY6. That’s why I choose to use it.
Fortunately, access to the NY6 is something that G5 teams could theoretically control if they consolidated the best teams into one league and started getting that autobid every year.