How simple are your bass lines that you can limp through that easily? I mean, if you're playing root note stuff, sure...but try something complex with a missing D or G string.
Crowds & club owners notice more than you do when there's a lull. A 10 second lull feels like a minute to the crowd. Given that on most basses, due to the bridge not being a quick release, a string change will take close to a minute (including time to find the string, open the package and get it on). That's not worth potentially screwing your band out of return gigs or having your dance floor clear out. Your livelihood, and your band-mates' is on the line.
My guitar player got a new Gibson LP in the summer and we had 3 gigs lined up after he got it. 1 of them was a wedding for a friend and we had to take a 10 minute break for him to restring. I started carrying my Strat as a spare for him to use, as he couldn't justify having 2 guitars (even though he saw the point we were trying to make). Needless to say, he broke different strings at the next 2 gigs & needed to use my Strat.
He's since had the guitar looked at & rounded over the saddles a bit & fixed the break angle, but he would have been screwed and we wouldn't have been invited back for more gigs if he hadn't had my backup.
Do you really have the whole band stop and do nothing if one person is unable to play temporarily for whatever reason?