Pizzas have thick or thin bases? I think that's the answer to your question ... there's no "or" about it, except in busy "pizza" take-aways and restaurants. They supply pizzas with uniform thickness bases that drop out of a rolling machine and perhaps get a casual (ineffective) twirl from the "chef". Perhaps the trend isn't towards thinner bases, but an increasing desire for a crispy base? A decent move ... but instead, the limitations of "fast food" outlets means they are getting a pizza topping on a biscuit.
In the same way as a decent Cornish Pasty doesn't have a uniform base, neither does a pizza. It's not even possible by hand shaping the dough (you can try by using a rolling pin ... argg, hisssss). They are thin based in the middle, thick and crispy (just the outer) around the outside edge.
Do yourself (and anyone with you) a great favour and make your own!