Ha! I would argue that NRBQ---in their classic line-up with Al Anderson playing guitar and singing, Joey Spampinato playing bass and singing, and both contributing songs---were not just the world’s greatest Bar band, but perhaps the greatest Rock ’n Roll band (Dave Edmunds, Nick Lowe, and Elvis Costello agree with me).
Rockpile could be too (I won’t mention yet again The Band ;-), but they lasted for only one album. Some may feel that honour belongs to The Stones, or The Who, or The Dead, or Led Zeppelin, but none of those bands are what I consider Rock ’n’ Roll. Many will disagree with that sentiment.
When Bill Wyman left The Stones, Keith Richards offered Spampinato a job in the band. Joey elected to stay in NRBQ. Gotta admire integrity, ay?