I think you've done the same thing everyone in this conversation does: an appeal to data. The problem is that the available data provides nothing but data. Seems like such a simple thing to prove.
One of my best friends shoots a .308 in prs and doesn't own an annealer. He brags about getting 11 firings out of his srp lapua brass without an issue.
I have another friend who brags that the 8+ firings he gets out of his srp lapua .308 brass is only due to the annealing process perfected by amp. They can't both be right, can they?
Like I've read so many times myself where, like your friend, claims made for getting good results without annealing are made. But there's so much missing information, like. . . how much expansion is being done in the chamber and how much sizing is being done to get an idea of how much work hardening is being done on each cycle. And yes, I'd say it's actually very possible they both can be right. . . particularly if the one not annealing has a custom chamber and minimizing the sizing operation (reducing work hardening each time) with their die. Compare that to a mass produced factory chamber and you're going to see big differences in how the brass works. So, when statements like that are made, one really needs to look much deeper into what's going on and not just look at it from face value.
It's like, I've so often read how bad .308 Federal LRP brass is, lasting only 4 or 5 firings, yet I managed to get 13 firings from my .308 Federal brass without primer pocket issue (except on just one case that gave up at 9 firings) and I was using moderate to hot loads. I think maybe that's might be because my chamber was a little tighter than theirs??? At 13 firings, I trashed the cases as indication of case head separation was becoming quite evident.
If you don't have a gun that shoots better than 1 MOA, I don't think annealing makes any difference. But in a gun that can shoot less than .3 MOA, yes!

In that link I posed with a video of testing, I took that data a few years ago and put it on a spreadsheet to get a better idea of the issue we're talking about. Here's those numbers: