"A gigging musician should always carry backups."
Y'know, I've heard this since I started playing again twelve years ago. Early on I followed this advice. As time went by I came to believe that the "always carry a backup meme" is a crock. (No offense intended if you follow this advice. It's the meme that I don't care for; I have no issue with your practices.)
The supporting argument that I usually see is that an entertainer can't afford any downtime ever. If a string breaks, I'm supposed to be able to pick up the "spare" guitar and keep playing before the next chorus rolls around. Ditto being able to switch to a spare amp.
The corollary to this argument is that it's "professional".
The thing is, there's no real definition of "professional" behavior for musical entertainers, is there? It's a circular argument: one behaves professionally because one carries backup gear, and one who carries backup gear behaves professionally.
Aside from that, who says you can't take a break of a few minutes to deal with an equipment issue? Is your audience that unimpressed with your show that you absolutely must dominate every second of their attention lest they'll get bored and wander off? It seems to me that this - if it really is behind the desire to have spares on hand - is either insecure (on the part of the musician) or disrespectful (of the audience's ability to attend to one's performance).
Y'know, it's one thing for a professional traveling group that plays hundreds of shows in a year to carry spares. An organization like that needs spares. They can't afford to wait for a return-to-depot repair when the show has to set up night after night after night. And huge crowds do seem to have an unusually short attention span, so it might be beneficial to keep a smoothly-flowing performance.
But for those of us who play for a couple hours at a local venue once a week: would it really matter if we took a few minutes to replace a broken string once or twice a year? Heck, if we're in an ensemble the other band members could even vamp to cover our (infrequent) downtime.
I'm not arguing that we should be cavalier about our responsibility to put on the best show possible. In addition to being prepared in a musical sense, we should also take care of our gear to assure that downtime really is exceptional rather than commonplace.
But carrying backup gear as an independent performer...? I'm not sold on the idea.