How often does it happen to you?

Is that in the sidewall?
Almost. Another law of Murphy: It always hits the weakest spot.
Same with the bicycle tires: I drive puncture resistant ones, which at least reduce the likelihood that something penetrates the tire.
Quite often I picked up sharp object near the sidewall where the puncture resistant layer is thin or absent.
The odds of picking up a sharp object during the sharp turns that make up 1% of the total ride are great obviously.
This observation may be explained with survivorship bias however.
Likely the puncture resistant layer does a good job during the other 99% of the ride and I didn't notice how often it actually prevented a flat.
 
I once had a thorn go OUT through a sidewall.
It had gone in through the tread, and stitched the innertube to the tyre. I've dug plenty of glass out of marathon plus tyres, enough to know they definitely do work. I used slimies many years ago, good, but don't work near freezing; I think that they may work by the temperiture change as the air expands through the hole, but this is just a guess.
 
Some years back I thought having made a proper choice selecting Continental Ride Tour tires with an extra puncture protecting layer, but nope, after couple of weeks the rear tire had already lots of small cracks all along both sides, but thankfully it held until the thread was almost worn out ready for a replacement, and I had back then just bought a new pump with pressure gauge and pumped up to near maximum rating (did check the pressure with the tire pump gauges at gas stations to make sure my new pump wasn't too off, btw I prefer inner tubes with car valves), but no much safety redundancy there, shame on C..

https://www.continental-tires.com/bicycle/tires/urban-tour/ride-tour
Continental Ride Tour Bike Tire.png