Since I am currently working in an environment that resembles GP's premise, I have to say that I find this take to be way too optimistic.
I'd be exactly in the boat you describe (and actually: I've yet to see a situation where someone reviewing my code did not lead to improvements). But: If I want my code reviewed, I have to actually fight for it. Since everybody's workload is too high, even the willing often simply don't have the time.
From higher up, at our place, there's no one that actively opposes code review as a practice, but they don't seem to get that it requires investment (i.e. time), either. That means that if management refuses to change their ways of planning or explicitly enshrine reviews as priority tasks, it simply won't happen except for maybe the gnarliest cases.
And that's from a perspective of the change's author being willing and proactive. I work with individuals that produce very questionable code at times. And I'm not talking style here: Code in 2021 that still is prone to SQL injection at every turn. Methods that are hundreds of lines long with a gigantic cyclomatic complexity that no one (including the author) will ever really understand. Method names like "process" and "process2". And so on.
Needless to say, those programmers will never push for their changes to be reviewed. The rest of the team simply discovers them after they blow up (which they do regularly) and we're debugging.
Now, these people are luckily a tiny minority (which at least makes this somewhat bearable), but I over and over again would wish for someone with more authority to show that they're interested in the matter. Which a policy on code review would do -- if only as a signal. Yes, we want to check each other's code. Yes, we want collaboration. Yes, that's more important than some arbitrary deadline for minor feature X. Yes, we expect our programmers to be professionals.
Another symptom of such an environment also is the fact that everyone is the king of their particular hill. No one every familiarizes themselves with another person's code unless they really have to. By now, I've jumped to insisting that every change on a critical component I'll ever make will be done through pair programming, and so far, at least that seemed to stick. But again -- that only happens if both parties involved actively fight for it instead of everybody understanding that this is just an expected part of work.