Generally in such games it’s not a requirement to generate Plot Points via role playing (or getting yourself in trouble, rather) but since it’s an option it’s one players are encouraged to take.
Let’s take three examples of the Thing in different systems:
1) In many traditional RPGs, Ben derives no benefit from going on a brief self-loathing rampage in Yancy Street, but does derive narrative and reputational disbenefit from property damage etc. The player is discouraged from doing so unless it’s something he feels is important to do.
2) In MSH, Ben is penalised 50 Karma for going on a rampage (it’s actually one of the key examples in the book) as well as all the problems from 1) above. The player definitely isn’t doing that unless he really feels he has to.
3) In MHR, Ben gets a PP for playing up his Man or Monster Distinction; he can later spend that PP on a variety of bonuses, such as the Clobbering Time FX (attack an entire crowd of mooks with one swing). The player is incentivised to at least think about having a rampage when it’s dramatically appropriate.
The three options result in different incentives and thus sometimes different player choices. Different tables will have different opinions about the three options and their play styles.
Personallly, I rather like 3) for superhero games because it tends to model what happens in comics better. There’s a mechanical reason Ben gets into a self-loathing funk, or Johnny is such a hothead, or Reed loses himself in his work, or Sue always tries to protect everyone. Sure, you can do all that with just roleplaying, but in my experience you get better and more dramatic results with 3).