Not everyone has washing machines at home here in the US. Some older houses do not even have the capacity for them, especially in terms with having a septic system set up to take the massive water intake. For many years, my parents used a public laundry. It certainly beat trying to wash clothes in a tub on a wash board, and they didn't have the wherewithal at the time to add the space for the machines, purchase them, and upgrade the electrical and septic, and didn't choose to go into debt to do so.
When I lived in an apartment in a rather large city here in the US, there was no washer/dryer, and the landlord didn't seem inclined to put in the hookups necessary. Again, I took my clothes to the public laundry, as it was a lot easier than imposing on friends or relatives to use their washer/dryer when there was a perfectly good alternative available elsewhere.
Once I could choose to have a washer/dryer of my own, I stopped going to laundry-mats -- because, let's face it, it's a heck of a lot easier to wash my clothes at home. The only time I might choose to do otherwise is when those appliances are broken down, or perhaps in a situation like returning from vacation or an entire house-cleaning where I have many loads that I'd like to do in a short time.
I suspect that mostly people go to public laundromats because it's what they have available to get the job done, not because they choose to do so over using their own machines. I saw a lot more of them in the Southern US than I do where I currently live.