I know people who have accepted 'being unhappy' as a part of their identity so I can what you mean about that.
For the perceivers, it just seems to me that if you don't have any expectations of things then there is less disappointment and if you are more flexible then there are more options that will make you happy.
It's really not that black and white.
All the J and P label identifies in MBTI is whether the first extraverted function in your function stack is a judging or perceiving function. That is it. I don't know who the hell came up with the idea stereotype that Perceivers were
all go-with-the-flow relaxed dudebros and
all Judgers are more like ruler-smacking school matrons, but neither of these assessments is remotely true. Mostly because these extreme ends of the judging and perceiving spectrum can only accurately describe EP's and EJ's. Everyone else is actually an inverted mix of these traits.
IP's, for example, very much do the 'should' thing because their inferior function is their extroverted judging function that is playing a tug-of-war with their dominant. While their outer-world appears a lot more easy going, their inner-world is rife with 'should's' and 'shouldn't's' .
IJ's, on the other hand, may appear judgier on the outside because they express their opinions and view-points in certain terms, but on the inside, they're a lot more accepting and have a less rigid processing system than their IP counter-parts. They're actually
less likely to impose rules or controls on themselves and prefer a more easy going, perceptive approach (characterized by their dominant perceiving functions) that is more of a 'let's see what happens...' until external pressure is applied.
In essence, IJ's and IP's are not actually pure judgers/perceivers, hence, your hypothesis that 'perceivers don't spend time thinking about what 'should be' and there therefore happier' is incorrect.... because both judgers and perceivers of the introverted variety do this. Just they process it differently.
But in general, all types are capable of making themselves pretty damn miserable in their own way.