Actually, Verizon doesn’t have to work with Apple any more than again, broadcasters work with Sony on their TVs.
You act as if service is broken everywhere, yet there are literally millions of iPhone 13 users in the metro areas you mention not having issues.
That doesn’t minimize your issues of course, but it points out the impasse. Apple is not going to break their devices because they work properly elsewhere; they are also powerless to get Verizon or any other carrier to fix their networks, just as they can’t force car makers to fix misbehaving CarPlay head end units. Apple would be happy to work with them but they can’t make them work on it.
You’re right, you don’t need to diagnose the issue, but all Apple can do is complain to say Verizon but Apple isn’t their customer, you are.
My comments aren’t to force you into diagnosing the issue, they are merely to explain to you what is likely occurring given the data and why.
As I stated, except for once, where a user was able to get Verizon to go out to their local tower and take readings at Apple’s and the user’s behest, every other iPhone 12 user who had the issue resolved had it fix itself one day with zero updates to their phone, or after a carrier settings update.