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I did the same, but put in a new tube and rejoined (is that allowed?)
If ya did it in the pits.
It doesn't matter really unless you are competing for places / league standing.
Tubeless helps with this but make sure you use the modern tougher tubeless specific tyres that have reinforced sidewalls, coz instead of wrecking a tube you might wreck the sidewall of tyre instead.
Unless you are going to win stuff I'd sneakily try tyres a bit bigger than UCI / BC rules determine, simply because it's such a bloody waste of time and money if you schlepp to a race then pinch flat on lap 1.
I did the same, but put in a new tube and rejoined (is that allowed?). Couldn't avoid coming last after that. Considering tubeless now.