That's how all these vendors justify their actions once they decide it's time to kill off their competition and impose arbitrary limitations. But how real is this "damage", actually? How big do you think the overlap between 'users who want to install custom operating systems', 'users who have no idea what they're doing' and 'users who would loudly complain after an obvious mistake on their own part' is? The #1 source of reputational damage for vendors is people breaking something within their controlled environments. The bar to run a custom OS is already so high for average people that it will never matter or be a social engineering attack vector, just because of how niche it is. We've been able to run anything on PCs for over 40 years, custom firmware for phones goes back at least 25 years, and despite all of this, the world hasn't gone up in flames yet. The security pressure exists, but it's minimal compared to everything else. The real reasons are profit-driven.

Do they even care about reputational damage?

Since you picked the phone as an example, right now when I search for ChatGPT in the Play Store, the top app is a fake app with a counterfeit logo. Is it really this platform which was supposed to improve security?