Punctured tyres are not a problem in practice anymore. Puncture resistant tyres are fairly cheap and very reliable. I cycled thousands of kilometers without getting a flat.
I've never had a flat tire in the countryside trips, though. It's always on broken glass some jerks throw at bike lanes in bigger cities.
Also probably the fact I'm overweight is a factor.
BTW when I was about 7 I had a small bike with full-rubber tires. It was great, I wonder why it's not done for full-size bikes. It wasn't THAT much heavier.