Tagging along and not making a skill check is just another form of staying back at the inn. Bob is still not participating. He's shut out and has to stand there watching while the charismatic types carry the ball.That doesn't actually illustrate a difference between "X successes before Y failures" and "X successes in Y passes". Bob the Silent could tag along with the first group (X success before Y failures) and not make a skill check just as easily as he could in the second.
With "X successes in Y passes," Bob is an asset to the party, however small. He can participate. He has an incentive to do whatever he can think of to help the party. If all he can come up with is to stand there looking imposing, fine--he can try an Intimidate check at DC 15 to impress the king with his quiet confidence. He'll probably fail, but there's no penalty for failure except opportunity cost. Taking a long shot is better than doing nothing.
With "X successes before Y failures," doing nothing is better than taking a long shot. Bob's worth in the skill challenge is zero. The best thing he can do is sit down and shut up. If the king turns to him and asks him a question, his worth goes from zero to negative.
In the second (X successes over Y passes), if they need to get 3 successes out of 4 PCs on one pass, they still have to make 3 successes before 2 failures. 2 failures with 1 pass over 4 PCs means that they can't achieve 3 successes on the pass. If Bob the Silent tries to get a lucky roll and blows it, they're one failure closer to blowing the skill challenge.
Your logic is based on the assumption that all four PCs are participating in the challenge. Take that away, and it falls apart.
Let's say you need 3 successes on 1 pass. Which party members should participate? The obvious answer is "all of them," because you get 1 roll per PC. If you have three PCs involved, they all have to succeed. No one has any room to fail. If you add Bob the Silent, and one of the first three PCs fails, it's just possible that Bob could pull things out with a meaningful stare and a natural 20. The party's chances are better, if only a little.
Now suppose you need 3 successes before 2 failures. Which party members should participate? The answer, if you can swing it, is "Lucky the Loquacious, bard extraordinaire, and nobody else." Lucky has the best Persuasion check, therefore you should let her do all the talking and make all the rolls. She's almost certain to get 3 successes before 2 failures. Every other party member is a liability dragging Lucky down. If you can't convince your DM to let Lucky go it alone, then at the very least you should try to keep Bob out of sight.
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