Because every company says "we take quality very seriously" and standard crap like that, looking through the code and the most recent contributions is the only way to actually assess them.
> It makes me wonder if they’re inflexible or unwilling to be pragmatic about imperfect code.
Which is perfectly reasonable when the hiring companies try to avoid being pragmatic about imperfect people. They'll give stupid codes tests and look for rockstars, this is the employee equivalent. Rockstars are picky about their collaborations.
> Can they really learn anything about the codebase in the limited interview time we have? They’re not getting repo access.
Ideally I'd want to run some tooling over it and get some stats like cyclomatic complexity and collaboration graphs to see how many pointless layers they have. I'd also take a look at their unit testing to see if anyone in the company actually understands what a unit tests is.
Interviewing is meant to be a two-way street and code review is the only way to address the information asymmetry and make this true.