What having Brendan produce really is is having someone in the room that can act sometimes as an authority figure, sometimes as a tie-breaker, and sometimes as a collaborator.
When you're self-producing or when you're the producer's meal ticket, you don't have someone that has the position (or will) to step up and say, "This needs to change," or "This sucks," or "Try this".
STP's self-titled sounds really good. But sonic achievement isn't necessarily all you need a producer for. Brendan, especially because he is a great musician, can not only help you with arrangements, but also what is good and what is bad. Brendan may have pushed the band to make some changes to songs or to ditch a song in search of writing a better one.