I would think, that a back up machine is only useful in a small number of situations. If you sew for a business, then obviously being without a machine for any length of time, however short, is not feasible. Or, if you attend classes or retreats very regularly, then a smaller machine for travelling, would be useful. Beyond that, I just can't see the point.
I had a Janome 2010 for quite some time, until a Janome 6500P came into my life. For over 2 years, the small machine sat unused in my cupboard, because the big one is so reliable. I decided at the end of last year, that it was a waste. A good friend had a plastic'ey, very unreliable Brother sewing machine, and she was struggling with her sewing, mostly because of how terrible the darn machine was. I quietly gifted the machine to her, so that she can feel more successful with her sewing, and I haven't regretted it since.
That said, I do have another small machine, that I have used in the lounge (in front of the telly), although it isn't really a "back up machine". Its my Featherweight 222, that I recently had serviced. Sewing on it is more for fun that necessity, but it doesn't really back up my big modern machine.