We are more aware of the Play Integrity check now because GrapheneOS shows a notification for each attempt. However, it seems that some apps check even more things in order to ban users.
Mainstream app developers and companies are not blocking anything; former users generally keep their apps working. Some users are always lucky enough to claim that the app worked for them.
Conversely, new users and those installing an application for the first time with a VPN and an alternative operating system are increasingly encountering blockages. The more attempts you make, the more likely it is that you will get locked out.
I understand now some people on this forum having two phones (one with the stock Pixel OS), even though I don't like this idea of having two phones or going back to stock.
The GrapheneOS team is doing a very great job hardening the AOSP. But for "security reasons" apps and Google ask to downgrade the OS security.
Users who value their privacy are getting banned by both the app and people who insist on using only one particular application.