Should root canal treatment be done on the supporting teeth for a bridge?

No.: Unless the particular tooth is essentially gone and can't be crowned or fixed on own and be stable, no.

Possibly: It is not abnormal for a root canal to need to be performed on a supporting (abutment) tooth of a bridge. If the nerve is inflamed or infected, the root canal must be performed. The only other option is tooth removal and loss of the bridge.

Depends: If the nerves of the supporting teeth die or develop "irreversible" symptoms like waking you at night, aching throughout the day, etc, then yes, they would probably need endodontic treatment. But in general, just because a tooth supports a bridge does not mean it needs a root canal done.