Yes, happy people get easily worn down in bureaucratical organizations.
Some of them adapt and get cynical.
Some of them quit and join organizations where they can be happy and effective. It's the best part of my day to work among many of them.
I would describe myself as 'optimistic' rather than 'happy' but, in both cases, these businesses sucked the life out of me and the happiest days were when I left. Both times to my initial financial detriment.
Neither business is currently operating though, so no loss to me long term.
This is something that worries me on occasion. Certainly very few would intentionally do it, but I fear there could be some alligator-brain crab bucket game going on in the subconscious where some team members will be inclined to "even out" any happiness deltas across the team.
In my experience - not all unproductive people are complainers - but almost all complainers are not productive.
The productive people are proactive and start making change rather than complain.
I haven't met a lot of unhappy proactive people.