If a typical Amateur Radio repeater's ID'er goes down, can the users of that repeater ID on behalf of that repeater? IE,"this is Blah Blah Blah on the Blah Blah Blah repeater". Maybe I'm wrong but I have always been under the impression that a transmitter has to be ID'ed by the control operator or the transmitter itself. If one isn't the control operator, and I don't believe repeater users are, I don't see how that would Part 97 compliant.
A repeater has to be under local control, remote control, or automatic control. (Repeaters can use more than one control method.) If the repeater is under local or remote control, then the trustee or a licensed operator designated by the trustee is supposed to monitor the repeater at all times, and identify the repeater and otherwise ensure that it's operating legally. Let's call the trustee and licensed operators designated by the trustee "control operators".
These requirements for local or remote control are an obvious burden: if a control operator can't monitor the repeater, even for just a short time, then the repeater isn't legally allowed to operate. This explains why automatic control is by far the most popular option for a repeater. With automatic control, the repeater can keep running even when the control operators are asleep, at work, or using the toilet.
With automatic control an automatic mechanism, the repeater controller, is allowed to automatically handle many of the legal requirements of the repeater, such as identifying. But the trustee is still responsible for ensuring that the repeater is operating legally. If the repeater isn't identifying, then the repeater is no longer operating legally under automatic control, and then the trustee would be legally responsible to either shut down the repeater or see that the repeater reverts to local or remote control, with all the rules that come with those operating modes.
From a practical point of view, if the repeater isn't identifying then the controller is broken, and the trustee or a previously-designated control operator should be notified ASAP. The trustee would probably appreciate people identifying the repeater manually until the repeater can be shut down and fixed.
Having ordinary repeater users identify for a repeater with a broken controller wouldn't legally be enough to keep the repeater running, unless trustee-designated control operators (local or remote) were monitoring the repeater, and the repeater were shut down when the designated control operators weren't monitoring.
I think in some sense you are correct, users can't ID for the repeater. Unless the user's call sign is the same as the repeater's call sign, the user can't identify for the repeater.
However, it could be argued that in some cases, like for instance, a small cross band repeater which typically doesn't ID, the user might actually be the control operator, so that is probably OK.
However, if you are saying "this is the XXX repeater" on the input frequency, what comes out the output frequency is ok, but what is on the input frequency is not correctly identified, so that's not right.