It all depends on where you lived and where you rode your bicycle. In the Southwest we have a weed that grows wild. It's everywhere, and during the hot desert summers it dies from the heat and little thorns fall off. They get in your feet when walking araound bare foot. Dogs pick them up, etc. They are a real nuisance. Maybe as we have spread out our cities, and built houses, streets, sidewalks, and paved everything it might be a lessor problem today.
I grew up in Phoenix, AZ as a kid. We rode sew-up tires on our road bikes. We were very careful to not ride on the extreme right edge of the road, and never rode on dirt. One accessory that was on many of our bikes was a bent wire scraper that was attached by the brake center bolt. The scraper was adjusted to ride just above the tire tread and scrape off the broken glass and thorns before they could make a couple of rotations of the wheel. They were kind of cheesy, but actually worked.
The thorns were as sharp as cactus.
John