but it’s not like they add it for no reason.

I didn't say anything about that. I'm saying the main reason Bethesda removed Denuvo from Doom Eternal is likely because of cost reasons, not because it's a marketing play to drive sales (like OP suggested).

That's the intent behind it, how well does it actually work in that front well it's tough to say. Fact of the matter is I know this from hanging out in these communities people who aren't willing to pay for the game but still play it usually aren't willing to pay for it just to play it.

The actual amount of people who "give in" is tough to estimate, because many people who do it are either astroturfing or are pretending, and most of the people who do "give in" typically will keep quiet about it, it's not in their best interest to Brand themselves as a shill to other pirates.

So the legitimate people almost never speak up about doing this, and most of the people who speak up aren't really doing this either. So it's hard to say just how much the DRM actually curbs it, and since the companies and their shareholders are paying for it they would probably want to imagine that number to be as high as possible because if it isn't they really are paying for it for nothing more than an imagined benefit.