About 10% of people are left-handed (and some studies say among Americans it's now closer to 13%). So if there is no disadvantage that means about 10% of successful QBs should be left-handed, too, right? That part shouldn't be too hard to figure out. Curious what the numbers would show.
In the NFL, there are 36 QBs in the HoF, but only 2 of them are left-handed throwers (Steve Young and Ken Stabler). That's about 5.56%. Well below the representative % of left-handed Americans. It's an admittedly small sample size, but those numbers do say a left handed QB is less likely to make it to the NFL HoF than a right-handed QB.
I have some theories on "why" that could be (e.g., fewer available left handed coaches to teach the mechanics of the position, scheme issues along the offensive line involving protecting the QB's blind side, etc...). But it is similar to how being a left-handed pitcher is generally great (because most batters are right-handed and they see the ball later when it's thrown by a lefty and get less practice hitting against lefties... because there are fewer lefties). Or how being a left-handed first baseman is great (because your glove is to the boundary side and you don't have to make a turn to throw to second) while being a left-handed third baseman is meh (because your glove is away from the boundary and it takes longer to reset your body to make a throw to first or second base).