I think this is a valid point. If we're playing for distracted or disinterested audiences it would better, both for the band and the audience, for the band to AT LEAST play songs that they love instead of just regurgitating the old overplayed standards all night long.
The point to me is that there's a reason audiences are distracted, and the band can (usually) change that if they want to.
If the band is disinterested or expecting something from the crowd from the moment of downbeat, they're going to convey that disinterest or disappointment and the audience will mirror that right back.
When I am about to start a gig, I take stock of who's there, I walk up to anyone I might know and chat them up a little and thank them for coming out, and I remind myself that I am there to have fun, even if there are only three people there. Those three people made an effort to be there and I am there for them.
An empty room is an opportunity to rehearse with all our stage gear, and the band can have fun with that.
If you're up there worrying about whether or not you're going to be asked back, or how many people are there, or whether they're paying enough attention, it doesn't really matter how much fun you're pretending to have - your disappointment and anxiety shows. I know this because over the years I have been that person who worries, and I have worked with that person who worries, and I've seen the difference between the nights when the worrier was happy and the nights he was not. Nowadays my only goal is to have fun up there and I make sure my bandmates know that, too. I don't want them fixating on their mistakes or imperfect stage sound and dragging stuff down. Brush it off, nobody cares. We're there to enjoy the moment.
I'm editing to add that, at a wallpaper gig, you're not really expected to engage the audience and distract them from other things going on. So that would be a somewhat different sort of gig, and an opportunity to have fun in different ways.