Hey @Max Stewart
Assuming you are referencing shared mailboxes here.
Exchange needs to store data about the mailbox in question and has always used Azure AD/ ADDS to do this via attributes.
As such, you technically can log into these mailbox and this is sometimes a requirement for services to integrate with your mail service.
Logging in like so isn't a desired scenario and application of MFA should occur against the user account who is accessing the shared mailbox.
From the About Shared mailboxes page:
"A shared mailbox is not intended for direct sign-in by its associated user account. You should always block sign-in for the shared mailbox account and keep it blocked."
See the following links for more detail:
Block Sign-in for the shared mailbox account