Are there ("not insignificant") security implications to using the same OTP secret across multiple servers?
On my network, I'm running gitlab-ce, nextcloud, and LTB self-service password among a few other services. GL and NC both support 2FA via TOTP, but as individual add-ons and not via a central auth (such as LDAP) or some other shared way.
I'm working on a PR to SSP to enable 2FA for the password-change, but then I wonder if it'd be possible to have GL use the same LDAP-stored OTP secret. I want to suggest supporting this to GL, but only if it does not weaken the system.
The consequence of not centralizing it is not huge: each app/server will store its own 2FA secrets, so the user must manage them all individually. Unlike passwords which don't technically require a password-manager, I don't know of anybody who is able to remember their OTP secret and generate codes in their head, so users are forced to use a managing app (such as Google Authenticator or FreeOTP Authenticator). Reducing from a list of multiple secrets to one is mostly just convenience.
Similarly, besides convenience, are there known advantages to centralizing OTP secret storage?