Like sure, you're usually going to start the design review with a prepared document that everyone's looked at in advance, but if it becomes contentious, you need people to be able to quickly pitch their alternatives and hash out the various tradeoffs in a synchronous way (eg, not running off and making a whole new slide deck for each stage of iteration).
And I 100% think that both parties getting a feel for how work is done is very important, so I think like letting interviewees have a look at some code reviews, maybe sit in on a retro, do a pair exercise or whatever, this stuff makes sense. And I like your point about "if things become contentious": a lot of teams can fall apart in these moments, and they're kind of a test of the maturity of the participants and the strength of the culture.
For example, I'm fully against whiteboarding now. I'm pretty good at it, but I think it's irrelevant and ableist (lots of people have anxiety issues and so on). When companies ask me to take a live test, I decline respectfully, talk about all this, and offer alternatives (pairing, take home assignments, review of past work, references). If this doesn't fly, well it wasn't meant to be, and it's better we both found out early on.