Obviously the quality is already very high, but still quite a ways to go for each batch consist of "50 AirBnBs", which to me is a far more impressive goal than having 1000s of lower quality startups. It's also better that YC is a signal of success than "not-YC" being a signal of failure. Franchising would dilute the brand and more importantly be a distraction from (as YC would always say) making and improving something people want.
YC is relatively "open-sourced" and there's nothing to stop others from creating accelerators with similar models around the world (and in the valley). There are already hundreds of imitators and these catch many of those that YC misses.
a.) you would say that, wouldn't you, you'd like as much of PG's attention as possible
b.) it's quite presumptious to state that the 1000s of others would be lower quality. Are the less than 1000, mid 20s, mostly male, mostly american, applicants to YC the best candidates on earth?
There are probably 1000x, if not more, capable founders of all age groups, nationalities, and genders that PG could get a slice of. He's built a brand and should seek to capitalize on it before someone establishes a superior brand.
Off course, this all about what PG does for fun, he's already rich enought to never work again. It might be that he enjoys mentoring a few founders a couple of times a year and doesn't have global ambitions.
Harvard "built a brand", but I don't see Harvard establishing franchises around the world to capitalize and satisfy it's "global ambitions". It's satisfied with trying to be a better Harvard, which is why it's brand persists.
In the same sense, YC could scale by getting more of those 1000x capable founders to apply the regular way and continue to improve on picking the best of them.
However, from a purely profit perspective, PG would stand to make a lot more profits from scaling. After all, Walmart is younger than Harvard by hundreds of years, but makes a lot more money.
If there was a YC here in Costa Rica the startups would be heading to SV to raise money. Multiply that by dozens of other countries that can't provide the complete ecosystem and the name becomes worthless and the network no more beneficial than HN.
I think YC does extend its' brand in a different way: by funding companies that create new avenues for startup funding/networking such as FundersClub.