As I see it, it depends on how one approaches this matter. On the one hand, you can be a purist and insist that a pizza be defined by its origins, for example, the types of pizzas that were made in Naples and maybe elsewhere in Italy and that inspired the pizzas that were later to be made in the U.S. The ingredients would be simple and basic--mainly flour, water, salt and yeast--and with simple and modest toppings indigenous to the areas where the pizzas were made. On the other hand, one can view pizza from a commercial perspective where the objective is to make a profit. When viewed from that perspective, almost anything goes. It is much like how bagels were transformed from something hard and chewy into a softer medium for sandwiches, and yogurt was turned from a sour, tangy standalone product into a sweet dessert like product. Once the objective is to make a profit, then just about any transformation can be justified.
I remember when, several years ago (in 2004), I started a thread called Pizza with an Egg. That thread is at http://www.pizzamaking.com/forum/index.php/topic,637.0.html
. I did not out and out call the pizzas I described in that thread "egg pizzas" (other than a few places to shorten the expression) because I wasn't quite certain that putting eggs on a bread-like base made them into pizzas. However, if you scan the photos of the pizzas shown in that thread, you will see that I found a way of putting eggs in several different forms onto a pizza base. The inspiration came from several different food disciplines. At one point, at Reply 28 at http://www.pizzamaking.com/forum/index.php/topic,637.msg14353.html#msg14353
, Bill went so far as to suggest that what I had done did not represent pizzas, although he saw merit in what I had done. All I remember is that I liked my eggs on pizza creations. There was even one with a bit of whimsy, at Reply 25 at http://www.pizzamaking.com/forum/index.php/topic,637.msg8886.html#msg8886
. Maybe that one doesn't deserve to be called a pizza but it was a lot of fun notwithstanding.