I suppose if you were going to cut it close and there was no bag drop line, it could make sense to use the home tag. But ordinarily I don't see the point.
SFO a couple weeks ago was not letting people with self tag or home tag bags use the F/Elite line to drop bags even if they were in F or an Elite. I'd never had a problem with this before.
The bag drop line was very long and since the F/Elite line was much shorter, after getting scolded and being told to go to the bag drop line despite being both F and Elite, I took off my tag and told the agent that I'll be doing a full-service checkin instead. She was literally speechless. I had them generate a new tag at the counter. It was much quicker than standing in the bag drop line.