Marisol Doyle wasn’t bothered by the frozen dough and canned mushrooms common in the pizzas she ate as a kid growing up in Sonora, Mexico. It was comfort food.

“But as an adult,” she said, “I wanted something better.”

Ms. Doyle’s first experience with better pizza came in 2006 at Pizzeria Bianco, in Phoenix, and it was probably a lot like yours. Mozzarella that melts into pools. Crust that invites comparisons to fresh bakery bread. These are qualities found in the Neapolitan-style pies served at the wood-fire-oven pizzerias that are now fixtures of urban America.

In recent years, they’ve become fixtures outside cities, too, drawing diners to the types of small communities — from southern Illinois and coastal New England to rural Wisconsin and Oregon — whose restaurant cultures are often dominated by national chains. All those fussed-over pies, with their blistered crusts, basil sprigs and hot honey drizzles, taught Americans they could ask more from a dish routinely eaten from a cardboard box — and consumed by about one in eight people on any given day, according to U.S. Department of Agriculture research.

That broad appeal, coupled with the relatively low cost of opening pizzerias and the ease of acquiring the information to master high-quality pizza-making, has made the dish a uniquely effective vehicle for chefs to find a voice while also making a living. Until recently, chefs looking to make sublime Neapolitan pizzas would have few options beyond traveling to Italy, said Chris Bianco, who opened Pizzeria Bianco in 1988.

“Today you just swipe and study and you can bring great pizza to any town, anyplace,” said Mr. Bianco, who is arguably the country’s most influential pizzaiolo.