We did a street dance this last summer. It had been heavily advertised (including TV) and was in our lead singer / BL's hometown. Almost as soon as we got there things started going wrong. There was a wiring issue with the venue-provided power that blew up one of our power amps, half our light show and most of our rhythm guitarist's gear as soon as we plugged in. We had to re-wire our IEM system because some of that gear had fried, so the whole band basically had to share one mix. We were troubleshooting and jerry-rigging up until about 20 minutes before the show, in very hot outdoor conditions. Suffice to say that stress was high.
It turned out to be one of our best shows ever.
So to me the bottom line is, the show is what you decide to make it. As long as there's enough functioning gear to do the show, you're being paid to do the show.
Also, in my mind anyway, there is a huge difference between avoidable and unavoidable tech issues. If the guitarist's amp craps out mid-show because he was too lazy or cheap to do preventive maintenance, or the drummer breaks a head and doesn't have a spare at hand, or the singer's wireless mic dies with no replacement battery to be found... those things are what really piss me off because that's just just a lack of personal responsibility and basic professionalism. OTOH if the venue power-spikes and fries gear that otherwise was in perfect condition, well, what can you do?
My band is kind of control freaks as far as "the show" goes and because of that we only relinquish production to a third party when it's a requirement of the gig. At least 9 out of 10 shows we roll with our own P.A. and our own light show and we run everything from the stage. We have wireless IEMs with a separate submix for each member so monitoring issues are pretty much non-existent. We bring backups for everything and sometimes backups for backups if the venue is especially remote. End result, except for rare occasions like the above, technical problems happen vary rarely and when they do they are usually addressed on the fly.