To take an example - would I want the current US government to be better at compiling information across all its agencies / departments? Absolutely not. What it does with its current level of consolidation is authoritarian enough that I'm not moving back there any time soon. I hear similar sentiments from my Hungarian colleagues, who are quite familiar with competitive authoritarianism in their own country.
Of course, this mistrust becomes self-reinforcing. I don't trust the US government, so I want it to be bad at its job - but then it's bad at its job, so I see it as ineffective and bloated and continue to mistrust it.
IMHO the only way out of this spiral is the hard way: a system must do the hard work to show itself trustworthy, and it must do so _before_ people will entrust it with the information that would make the job of being trustworthy easier. As with human relationships, it takes a _lot_ more work to repair trust than it does to break it. Unlike with human relationships, you also have systemic factors: the system needs an unbroken series of good, principled leaders; it needs to visibly and credibly punish corruption, not turn a blind eye; it needs to de-escalate divisions, not inflame them; it needs various institutional safeguards to work properly, not chop away at them; it needs to allow meaningful dissent and criticism, not crack down on it; it needs to learn from expertise, not undermine it.
Most importantly: the system needs to learn from its failures, and adjust the rules and incentives of the system itself to prevent those failures from recurring. This is generational work.