Based on the 32 Week 1 starters, here is a breakdown of their playoff performances. A SB winning QB will have to win 3 or 4 games to earn a title. Only 7 of the league's Week 1 starters have won 3 playoff games in their careers, let alone in a single post season.
GROUP 1: Haven't started a playoff game (Brissett, Fields, Richardson, Levis, Nix, Minshew, Daniels, Darnold, Williams, Young)
I would be surprised if players in this group had much chance of making the SB. I guess Darnold and Fields would probably be the leading candidates with MIN and PIT 2-0.
GROUP 2: Started a playoff game but never won one . . . all 0-1 (Tua, Herbert, Carr, Geno, Murray).
Carr, Herbert, and Smith are on teams that are 2-0, although I am not sure any of them seem primed for a deep playoff run. Between Groups 1 and 2, that's already 15 QBs.
GROUP 3: At least they've won 1 playoff game . . . but have a losing record (Cousins 1-3, Watson 1-2)
Not sure that the Falcons or Browns are looked at as true contenders (even if they might sneak into the playoffs).
GROUP 4: Won 1 and lost 1 (Lawrence, DJones, Love, Stroud)
Pretty sure the Giants aren't going anywhere. The Jags, Packers, and Texans should all be in the mix to make the playoffs, but these QBs haven't shown they are playoff warriors yet. It doesn't mean they aren't, but they are relatively playoff unknowns.
GROUP 5: Won a couple of playoff games (Mayfield 2-2, Hurts 2-3, Lamar 2-4, Dak 2-5)
IMO, these guys have had the skill set, pedigree, and rosters to have won more . . . they just haven't (at least not yet). I wouldn't be shocked if one of these teams made the SB, but I probably would be surprised if they won it. Groups 3-5 account for another 10 QBs.
GROUP 6: Won 4 post-season games and made it to a SB (Purdy 4-2, Goff 4-4, Stafford 4-4)
Stafford won a ring with the Rams, so hard to argue he couldn't win one (although not sure the Rams are strong enough to get there). The Niners have gone to the SB or NFCCG 4 of the past 5 years. They've gotten close. Many have the Lions as a top tier team. These teams could win a ring on paper, but not sure they could win 3 or 4 post season games in a row.
GROUP 7: Won 5 playoff games but not a SB: (Burrow 5-2, Allen 5-5)
I wouldn't bet that either CIN or BUF would beat KC in the playoffs. After watching the Bengals lose to NE, I'm thinking they may be a bit overhyped. Allen has had the Bills knocking on the door for 4 or 5 years now, and they haven't broken through. I think this version of the Bills is weaker than some of the others. Maybe Allen could will them to win . . . but he hasn't so far.
GROUP 8: Won 10+ playoff games and a SB (Rodgers 11-10, Mahomes 15-3)
Rodgers was on Packers teams that won 11, 11, 12, 13, 13, 13, and 15 games and didn't get to the SB (those teams lost 4 NFCCGs). GB won the year they won 10 games, but that was 15 years ago. I guess if the Jets get their act together, they have a lot of talent and a tough defense, so it's not impossible to think things could play out their way. I wouldn't bank on it, though. They're still the Jets.
The only other guy here is Mahomes. He's only lost 1 playoff game to an active QB (Burrow) . . . his other 2 losses came against Brady. Counting the rest of his games, he's a net +14 wins (15-1). The 31 remaining QBs combined are -8 wins (47-55).