Wider tires run on lower pressure. Lower pressure means glass doesn't push as hard into the tread and therefore do so less frequently. Not only that, when you get a puncture, it takes longer to lose all your air. I once had a puncture that I didn't fix until I got home since it didn't hinder me much.

I do see broken glass in the streets but long ago, it was much worse. The thing that changed it was the mandatory deposit law on bottles and cans in the 80s. I don't see all that much glass. Maybe I'm able to steer between the shards. And maybe my streets are different from yours.