Both of the last two posts are interesting. As a rock fan I've always heard the same debate about rock bands, that "friction between band members creates better music". And they point to all the big dysfunctional bands that have celebrated catalogs. But I think that's a misconception. The reality is that most rock bands are highly dysfunctional in the first place and so naturally a large number of the famous ones inevitably are too, despite the drama. But there are many many very successful bands that last decades without the constant fighting and drama, many who are actual friends. I don't think there's any correlation about conflict resulting in better music. The same thing with drugs. "Rock bands on drugs make better music". No they don't, it's just that a very large number of younger band members in their prime do drugs, so people mistakenly make the association.
So, as it pertains to sports, I don't think angry or loud fans incentivize the teams to perform better, but I do think they are a reflection of the expectations at those places in general. Every team inevitably has at least a few crazy outlier fans, but there's no question that some fanbases are more vocal and demanding at a large scale than others. Ohio State has not lost more than 2 games in a season since 2011 and yet after losing to Michigan again this year (and only weeks from another title) the fans wanted Ryan Day on a rope. Alabama already wanted to burn DeBoer's house down during his first season but even the previous year with Saban after all he's done the fans were merciless to him, and he won the SEC and nearly went to the NC game again. The more a coach or program does, the more that's expected of them. They don't build a cushion; they only build higher demands.
But at A&M I never detect any visceral anger, and in fact, things are celebrated in a way that are criticized at other places. It's kind of a running joke but the "We're the best 2 loss.. I mean 3 loss.. I mean 4 loss team in the country!" Or "Two of the teams we lost to are in the playoffs!' or whatever. Jackie Sherrill is revered as some kind of legend here and is the perennial answer to fix the football program ("If we only had Jackie back!"). Even putting aside the scandals, he went 52-28-1 and won all of two bowl games (against 8-4 teams) and then disappeared into the coaching pasture for good before the end of the 80s. But he's considered "The Standard". Meanwhile Mack Brown goes 158-48 and is in two national title games and wins 10 bowl games and even after 15 years of absence the anger at him is seething for underachieving. You can go to the Texas fans sites even in recent months and see "I'm fine with Mack glad handing with donors and passing out cookies at games. Keep him the **** away from everything else" and "Mack Brown can suck it". and simply "**** Mack". It's almost all because of the record against OU and not winning multiple national titles. Beating A&M 10 times gained him nothing except anger at losing the other 4. There was a running thread in recent years just to mock him whenever North Carolina lost.
So, I don't think fan anger helps teams at all, it's merely a reflection of what the fans have been conditioned to expect. So you get "Jackie went 5-2 against Texas, he's our hero!" at one place and "Mack went 10-4 against A&M.. is that supposed to impress us?" at the other.
And it's about the same for baseball.