As many have said a puncture is the luck of the draw and not the fault of the tyre size or profile.
20 inch tyres are such common place these days the manufacturers would have made allowances for low profile walls to be strengthened to ensure they survive most driving requirements.
You’re more likely to bend or crack a cheap rim than damage the tyre.
I’ve been running 20’s for 10 years and currently have them on a number of cars and have not had a single puncture or tyre go flat and I put that down to luck.
I have recently had an 18 inch tyre on my BMW lose pressure due to a faulty valve, a nail in a 15 inch tyre on my Torana that required a plug and I did crack two cheap 18 inch Chinese rims on my VS Clubsport a couple of years back when the grate from a drain had been washed away during a storm on the M4 in Sydney and I put them all down to bad luck.
I do run low profiles as you can see in the photos below, these are 285/25R20 on my Merc and I’ve had these for 6 years without a hassle.
I admit I live in an urban area being the NSW Central Coast but the roads are far from perfect and I do visit my family in far North West NSW a couple of times a year and the roads in some places are a shocker and the 20’s still work well.
One thing my tyre fitter has always told me which is contrary to what I often read and that is your rims will have a better chance of survival if you decrease the tyre pressure to allow the tyre wall to flex instead of sending the shock into the rim and possibly damaging it.
I’ve followed this advice for years and hit the occasional pothole and had the rims survive.