Skinny Tyres - Use once throw away?

Last Sunday I was out on the Trossachs ton and got a front tyre puncture from a piece of glass. It made a small slice in the tyre about 3-4 mm enough to cut some of the banding so that once re-inflated there was a slight bulge marking the puncture point. Now, I've taken the decision that, on safety grounds, the tyre is getting binned as I wouldn't feel comfortable descending on a tyre I know is not 100%.
The question is, is this relatively normal for punctures on skinny tyres, ie one puncture and they're trashed, or have I been unlucky?
The question is, is this relatively normal for punctures on skinny tyres, ie one puncture and they're trashed, or have I been unlucky?
You've no won the Big Cup since 1902!
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Perhaps I should get a job where I have more work to do.
But, if it isn't too bulging it might come in handy for turbo use where you can use less pressure.
Kona Jake the Snake
Merlin Malt 4
To Michelin's credit, at the end of the ride the slit wasn't much bigger but again for safety and peace of mind I replaced it before the next ride.
That's why I keep a small section of an old tyre in my saddle bag. Weighs nowt but will get me back home if needed.
Easier than cutting-up old tyres