Interesting question/point.
I think the generalization is likely that most NY pizza is not very good - crust, toppings, the whole shebang - as opposed to only the crust aspect. For example, I know that you have said you have to travel from one borough to another to get pizza that you think is good.
There is surely bad pizza in NYC, and it mostly resides in the gentrified neighborhoods of Manhattan. Diluted process, cheapened labor but as with anything there are also exceptional NY slices. Alot has changed in the past 20 years, and places like Time Square has become a corporate disney land, downtown has gone thru severe dilution. Soho is a mall. All ethnic cuisine in Manhattan has diluted, it's not just pizza. Chinatown is where you get fusion Chicken and brocolli, Latin cuisine is a joke and there are literally 2 legit Italian deli counters left south of Union Square. Little Italy is a joke. Many of the natives have moved out, and replaced with out of state transplants. But native New York City still exists in the outer boroughs and so do good slice pizzerias, and I doubt many forum members have experienced that having read through the discussions regarding NY pizza limited to Williamsburg, Best, Joe's Pizza etc type places which are mediocre tourist spots, and the dollar joints. There is certainly quite a bit of ignorance on this forum.
There are 2300+ NY slice joints in the 5 boroughs. Only 1/10th of them are in Manhattan. Surely there are hundreds of bad ones throughout, but there are also hundreds of good ones, a corner shop somewhere on Jamaica Ave, Queens, or 2 blocks off Arthur Ave in the Bronx, that the media won't ever write about, nor will transplants have the courage to visit because it remains an ungentrified neighborhood. The kind of rather be mugged by a fratboy on Union Square than someone in Washington Heights/Harlem mentality.
I have not sampled the wares of pizza places in NYC in a very, very long time, so my view derives from my readings here - especially from those who's opinions are highly respected.
Again, there is quite a bit of ignorance regarding NY slice pizza on this forum, and the sample size of observations on this forum is too small.
That begs the question of whether Walter's pizza (or anyone else's) is a "legit" NY Style pizza. Obviously, that depends on how one would choose to define it. And, whether others would agree on that as a standard, etc.
I'm 3rd generation New Yorker, my grandfather grew up in Kleindeutschland, which is today's Lower East Side, right at the cusp of Little Italy. I grew up in Yorkville, UES and ate pizza almost every day. Millions of other New Yorkers can tell you what is and isn't a NY slice, we never chose what it is, it just always was and all we did was eat it.. I can see your perspective as an onlooker, mostly dependent on other's anecdotal stories and descriptions of what the NY slice might be and how this could be more complicated.
NY slice pizza not complicated.. People who don't know what it is sometimes make it complicated and often define it into what they want it to be. Like an entrepreneur brainstorming a random pizza formulation for a shop somewhere in America and make one with characteristics that have very little in common with NY Pizza, but still attach a "NY Pizza" stamp on the marketing, there's something wrong with that imo or else we make no distinctions across any pizza styles and then why not call anything we want, Neapolitan Pizza or "VPN" too.
My belief is that the prevalence of excellent tasting pizza (in each part and the sum of the parts) has likely been changing towards the worse over time in NYC. And, the "composition" of the pizza (ingredients, process, etc.) has also changed over time. Not static, ever changing. So, my guess is that Walter's pizza is close to what was considered great pizza back in the "good old days." And, his memory and experience of that is greater than mine (and most others) since he has been in that business, in one role or another, for many decades. Building on that perspective, his pizza probably exemplifies what legit NY pizza is (or at least was).
Depends on who you talk to and keep in mind NJ isn't NYC. The NY slice I know at the old joints haven't changed a thing. But then there are now the Albanian owned places, and other immigrants making NY pizzas with no concept of the NY-Italian heritage, the same people who own Subways sandwich shops and the $1 joints. And past 20 years, you had advent of hybrid pies, made with different formulations, ovens, cold fermentations, etc (the Roberta's, Juliana's, Lucali's, Nicoletta, etc) to satiate hipsters and midwest transplants who grew up identifying with bready pizza.
And then there are some who will delve into stories of the origin of the NY slice as a reference point to authenticity. Some mention Mastro, then there are those within the Ray's Pizza lineage and Ira Nevin/Bakers Pride and mob heritage. Mastros was a franchisee/commissary model with frozen dough delivered to stores and then there are many independent family owned operators who never heard of Mastro and made their own dough and sauce. Who invented the deck oven? Who knows and who cares. Ira Nevin actually accused Blodgett/Mastro of having stolen his deck oven invention. The NY slice could have just been born of a collective movement of hundreds if not thousands of people converging into a thing. That said, most New Yorkers have no clue of the history, and could give 2 sh*ts but know what is and isn't a NY slice.
Perhaps, the way to approach it, is actually to look at pizza like Walter's pizza (including the crust) and think of it as the standard of "legit" NY pizza and judge the legitimacy of stuff that is sold today with that comparison.
Beyond that, in terms of trying to develop a standard from today's perspectives and experiences in NY - I do not know if there is a basis for a standard worthwhile striving to define and to achieve. I have my doubts.
I don't think anyone can fully understand a cuisine or culture unless having been immersed in it. That said my standard could be one of many pizzerias here, like a 50+ year old place like Margherita in Jamaica Queens or John and Joe's Pizzeria in the Bronx. The NY slice is archetypal, iconic, sacred. And what a New Yorker can probably do better is tell you what ISN'T NY pizza. Deviate too far from the original, or eat it with knife and fork, they will haunt you to no end.