Why did these corps implement TOTP?
To reduce support load from people getting their accounts hacked and asking support to get them re-instated. I don't doubt that these incentives also drive the push for passkeys, but passkeys are much more opaque and tightly integrated with the OS, and is thus more vulnerable to centralization.
why aren't these corporations locking down TOTP to restrict them to their own validator apps
They are. Authy is the biggest offender I know.
Edit: some info about how Authy locks you in: https://www.bentasker.co.uk/posts/blog/general/switching-to-aegis-for-totp-codes.html. Note that some websites integrate directly with Authy and force you to use Authy to set up the TOTP. The only way out is to use a rooted phone to transfer the codes to another app like Aegis.