Broken bottles are a real problem but good quality tires saves you a lot of flats. Not saying you can drive carelessly on any debris but a 30€ vs 10€ tire will be day and night. The Schwalbe Marathon Plus are the best known reference in this field. In my experience ”durable” tires from others brands are sometimes great and sometimes crap.
Also a regular bike checkup should includes tires checkup to remove the debris stuck in the rubber. Those can “move” and get you flat in the future.
I bike in Mexico. I usually get a flat patched with the bike mechanic for $1 USD and they do it in less than 5 minutes. They check the tire throughly to find the source of the puncture. More often than not they pull out a piece of metal debris from the tire (like small pieces of wire or nails). If the roads are cleaned, it will be a person with a broom doing it, which is why metal debris stays on the shoulder of the road instead of being suctioned by a mechanical cleaner.
Would good tires still save me from these punctures?
Gatorskins, as mentioned below are fantastic for most things, but in my experience they are not fully resistant to the damage you mention.
I've seen similar bike patching mechanics on sidewalk stations in Beijing, and I feel like they would have a similar primary customer. The degree of construction and infrastructure work there means that there are always metal bits in the road. Nails, roofing scraps, welding rod ends, filler wire trimmings that get washed off construction sites in the rain and blown to the roadside by traffic are highly effective at puncturing bicycle commuters' tires. But they also make small holes that are a quick fix. Soapy water will show where the leak is, and pliers, a donor tube, and vulcanizing compound and you're in business again.
Gatorskins are harder, less supple, so they don't pick up the smaller bits of glass and metal that will work in over time. They are resistant to pinch flats by having thicker, stiffer sidewalls, so the bigger bits of metal or rock aren't so scary ( they won't be any more fun, you will feel them more ). But a nail is a nail and if you hit it head on it will go in.
If a puncture isn't bad enough to require immediate road side repair then I'd say yeah, good tires should help a lot.
Thicker tubes can help, too. I use some really beefy tubes. They're way heavier but it's worth it to me. I went from a few flats a month to no flats a year, back when I commuted by bike in Austin.
I used to have those tires (before the bike they were on was stolen). A few years running daily in a busy city and I never had a puncture. You can go on broken glass and not have a puncture. I did exactly that a few times.
Current ones are some Continental with 5mm reinforcement IIRC. I came home one time with a piece of broken glass stuck in the tire. It was just stuck, pointy end in the tire but did not puncture it, so I just removed it and laughed.
Marathon Plus are great, but they're not the most supple of tyres.
Tubeless is a great solution for preventing punctures (especially sharp thorns left on roads after trimming of hedges and bushes), but it can be a faff to set up until you know what you're doing and the tyres are more expensive. You also "need" compatible rims to run tubeless unless you fancy a ghetto setup.
