I started experimenting with bromated flours vs non bromated 10 years ago. I did countless side by sides like what john fazzari is currently doing. Here is my take.
Bromated flours let you get a dough to the same point of gluten development with a shorter mix time, and give you crusts with more oven spring. Somehow even though the dough is "stronger" and has better ability to trap air, its also more tender. Bromate is especially useful if you are doing a thicker pizza thats allowed to rise a bit before baking. It makes for a lighter fluffier higher rising crust.
Just like john has mentioned, I have ended up finding ways to manipulate non bromated flour to give me a similar result, but in the end bromate acts like a crutch. Its more forgiving of under or over mixing.... too much manipulation during balling or shaping, improper proofing regimens etc. Somehow you can mess all of these things up and still end up with a nice tender crust.
The only negatives I can think of are that it does make a tighter cell structure in the end product (maybe a positive to some people) and that at a certain temp it starts to make the pizza too cottony in texture. That temp is probably around a 725 degree floor and higher, so most people wont even notice a negative unless they have a wfo. Before those temps even happen another issue comes to play which is that most (maybe all?) bromated flours are malted. This is why people use unmalted unbromated flours for neapolitan pizza.
My feeling is that every other pizza style (except for neapolitan, and maybe some people with very high temp coal ovens) can benefit from a bromated flour. Having said all of this... I haven't had a bromated flour in my house in two years since my daughter was born. Some will say thats overkill, but I have been able to make excellent pizza without it.