I've always believed that the Oye Esteban tour in 2000 (Boz, Alain, Gary, and Spike T. Smith) was the last time his band really felt like, well, a band. Once Alain and Gary left the scene, that is when the "band" became nothing more than a group of constantly revolving session musicians (sorry Boz, but its true).
I do remember the Oye Esteban tour.
The band threw some flyers to the audience for a second concert, but without Morrissey. They had a Rockabilly band and they played for maybe some 100 persons or less (can't remember the name of the band they had, but it was simply all the musicians who played with Morrissey, but playing Rockabilly songs.
I had the chance to talk to Alain Whyte & Gary Day after that Rockabilly concert (Morrissey didn't go to that concert). I actually had the chance to talk a lot because most people was not interested in them since probably everyone had gone there just to see if they could get an autograph or a photo with Morrissey, but Morrissey was not there.
Anyway, they certainly had the spirit of "a band"... well, they actually played as a separate band without Morrissey. The weird thing is that when I talked to Gary and Alain, they HATED Morrissey and they were very open about it.
I remember them telling me that they were upset because their contract with Morrissey didn't allow them to smoke or drink alcohol when Morrissey was present... as to give Morrissey a "clean image". They could not be seen with a couple or casual couple either as to keep the "celibate" image... and most of the time I talked to them, they simply complained about Morrissey and clearly considered themselves his employees... and not exactly "happy employees". According to them, they even had to follow a dressing code and considered that Morrissey was some sort of control freak who had made them sign an abusive contract.
So it is true that they felt like "a band", they actually organized their own gig, but Morrissey was NOT part of that "band" if you know what I mean. They were VERY open how much they despised Morrissey... and I do not mean playing with Morrissey, but mostly Morrissey as a person.
I think you are SOMEHOW right, they had the spirit of a band, but that spirit did not include Morrissey himself. They didn't like him and considered themselves to be his session "band".