alt Hacker NewsI'm pretty sure they both do have TOTP but it's not well documented that it even exists, and it's difficult for regular users to use. In iOS it in the Passwords app (née Keychain) and in Android I think it's buried in the settings app of all places. People don't know it exists and don't know how to use it, and even if they did, unless you're already using it for password management, it's difficult to know how to find it. Instructions usually default to a single authenticator app, like Google Authenticator or Microsoft Authenticator, so people end up with multiple apps (Not to mention the garbage adware that always pops up in app store search). And half the time the instructions simply say "Your authenticator app," which doesn't help Joe Schmoe who has no clue where he saved that OTP.
Many of the big companies seem to really want you to use their app so there's this big game of smoke and mirrors to avoid saying it is TOTP or what they're actually doing. And of course they make it as big of a pain to export your codes as they can get away with. Then they hide behind it being complicated and that is why they have to do this to help grandma, but much of complexity is due to their obfuscation.