If you care for your pizza, your customers and employees, you will stay in business for a long time, regardless of who opens a shop next door. Staying power, habits: those are huge positive factors for businesses.
“Mom and pop” businesses around the country show otherwise. A few restaurants with a very loyal customer base or outlier popularity might do well, but certainly not most. Same with hotels, rental cars, airlines, retailers, etc. There’s just advantages to scale that can’t be matched, and if there’s margin, someone is going to want a piece of it.