Before we get into it, let me just say that I understand that removing a major component of a dish may cause it to become something else. So cheeseless pizza may no longer technically be "pizza". To this I say: no one gives a fuck, please go officiate a spelling bee or whatever it is you do for fun, ya gatekeeping linguaFREAK.
I want to try to convince you to give cheeseless pizza a shot, because I think Big Cheese™ has been depriving humanity of the true deliciousness of pizza for millennia.
Cheese on pizza (and this includes the cheese substitutes that you might find on vegan or vegetarian pizzas) is like taking a carefully-crafted meal, flavoured and spiced to perfection, and then saying to the customer "hey, do you want me to dump a thick molten layer of bitter yellowish-white slime over everything? It'll completely overpower every other flavour on the dish, and will leave your mouth feeling weird and gross after you're done eating." and the customer is like "HELL YEAH!"
If you enjoy many toppings with lots of veg and whathaveyou, you are not getting the full experience when cheese is there cockblocking your tastebuds like an ugly friend at a bar. The sauce, the bread, the peppers, the onions, the 'shrooms, the pepperoni, they're all full of flavour and each flavour stands on its own and simultaneously complements the other flavours. Dumping a pound of cheese on top of it makes it all coalesce into a murky nondescript lump, something akin to trying to listen to music in a wind tunnel while wearing a thick deerstalker hat with the ear flaps down. It's like the difference between having an intellectually-stimulating conversation with a like-minded person, and trying to be heard as you discuss football stats with a drunk stranger in a bar where the sound system is cranked up to max volume at all times.
If you're someone who just likes a straight Margherita pizza, where cheese is very much the "main event", then this doesn't really apply. I concede that even the most delicious pizza sauce and most fancy base bread are not quite enough to blow anyone's mind with flavour if that's all you're working with. But if you like adding toppings, allow them to be the main event for one day, and when you do, give yourself over the involuntary urge to start singing A Whole New World when the flavours awaken hitherto dormant olfactory neurons that you didn't even know you had.
In many online pizza shops, you can untick "cheese" when choosing your toppings, and they'll respect your choice, and you won't receive a wellness check from the police or anything. You can do it with Domino's, and many of my local pizza places do it, too. You can also buy frozen pizzas sans cheese or cheese substitutes, although this is fairly rare (they think removing cheese means you need to replace it with some other gunk that does the same job, which is obviously not helping matters). And of course, you can make or buy bases and build your own pizza at home.
Try it. TRUST ME BRO.
#FuckCheeseOnPizza
Fun article that kinda sags off reality, so let's give it an updoot! (check the sublemmy name, haha)
I'm disabled now, and rarely make much pizza-from-scratch anymore, but I'm totally with you on the experimentation aspect. Way back when, I was in fact educated upon the idea that early pizza (or progenitors) were basically flatbread, featuring olive oil, herbs & toppings, with a classic one including fruit slices! (like figs)
Cheese was a later addition, and the basic template may go back to Ancient Rome, I forget, exactly.
https://thecozyapron.com/wp-content/uploads/2016/06/crispy-prosciutto-flatbread-pizza_thecozyapron_06-12-16_featured.jpg
But, no-- it's never easy to just handwave-away cheese like it doesn't do some critical things in modern pizza, such as adding a boatload of umami, unifying texture that wraps the whole dish together, and adding a pleasant chewiness that's very hard to replicate with almost anything else.
Me, I've tried any number of restaurant-grade cheeseless pizzas, and I've also substituted all kinds of things in my personal experiments, but it's never the same, and never even comes close, really. That said, cashew-butter enhanced with some MSG, garlic powder and ingredients X arguably comes closest.
Also, let's not forget that just as cheese became super-popular upon pizza, proto-pizzas didn't originally have cheese, and can arguably be perfectly-well enjoyed in flatbread form!