1. Don't think of themselves as self-interested arseholes.
2. They are in fact self-interested arseholes.
We have no methodology that allows us to put "good people" in power. And even if we had, power corrupts. So the best we can do is to build a system that works even when all actors are self-serving.
Doesn't seem to be working though eh?
That being said, I don't have any fantastic suggestions either. :(
Typically you just fix a bug, though of course some systems reach a point where a rewrite (either incremental or from scratch) is the only option. I see absolutely no evidence that we reached that point, all arguments are just emotional factoids. I also see no attempts for an incremental rewrite, all people want is to burn the system and hope that something good rises from the ashes.
It's almost like being a public company vs being a government run entity isn't the major decider of effectiveness / optimal outcomes for end users.
Instead, it seems to be "is this company (etc) run by self-interested arseholes trying to enrich themselves at the expense of others?"
If it is, then the structure isn't going to matter. End users are going to have a bad time, regardless of the PR/bullshit said company puts out to say otherwise.
Likewise, if the company (regardless of structure) is run by clueful people dedicated to actually providing the required service, end users are going to be in a decent position.
Unless of course they get screwed over by above mentioned arsehole types. eg starved of budget if they're a gov org, have activist investors cause trouble if they're a public company