Does this really have anything to do with GOS and more to do with apps not wanting to run on rooted phones? A rooted phone is more likely to be tampered with and have its sandbox rules relaxed. There's a big business of security companies selling tools to harden mobile apps and the bare minimum is not running on rooted phones.

A normal GrapheneOS installation uses Android Verified Boot with a locked bootloader, and does not give the user root access. Google's Play Integrity cannot be used to verify the integrity of the OS (as GrapheneOS is not approved by Google), but equivalent verification can be done using standard Android APIs and GrapheneOS's public keys.

GrapheneOS doesn't give you root access.

The OS is designed to offer privacy and security guarantees, which root access breaks, so they don't offer it.