Is a "yellow-tag" really necessary?

Andre wrote:

Ok, let's say my TSO'd Attitude Indicator (AI) in my Cherokee goes
belly-up, and my friend just happens to have one he removed from his
machine a month ago as part of a complete panel upgrade. We both KNOW
the thing works fine and would solve my problem.

What's the ramifications of just having it installed in my Cherokee?

This is exactly what I did with a DG. Someone on these boards was
gutting the panel and going with all new stuff. I bought the DG because
the one in my plane was acting up. Just swapped it out, didn't bother
to log it and away I go. There is no reason to have a yellow tagged part.