While I do think it's a decent idea to have at least one backup instrument at a gig, in nearly 30 years of gigging (including a lot of years as a touring sound engineer) I've only ever seen what I would call show ending failures of instruments (i.e. more severe than a broken string or dead battery) a handful of times. It's never happened to me as a player. IME, the vast vast vast (vast) majority of equipment failures on gigs are cable failures of one kind or another. This applies to instruments and amps on stage and to PA and lighting equipment equally. If something isn't working at a gig, 90% of the time it's a cable issue.