It's not as integrated as it could be, but it accomplishes the same thing.
Verified address(es) sound like the only answer, and that brings up another set of problems to solve.
Beyond that, just because UPS offers a membership doesn't mean that retailers will have it integrated into their checkout flow/logic. In a lot of cases that would be a re-work and could take a long time before it was practically usable.
Below constitutes my (limited) experience working as an engineer at a company with a big logistics component (not Amazon).
When you run an operation the size of Amazon (or even muuuuch smaller) and are putting out a lot of freight for UPS/FedEx, you batch up your outgoing material based on ship method and 'next hop'. In order to speed up the delivery from a 3-5 day window to a 2 day window, you would have to explicitly purchase the '2 day' shipping option for that customer, or it would get batched in with all of the other 3-5 day goods, which could get sent to a totally different distribution center than the 2 day.
We're talking huge numbers trucks all going to "Indianapolis 2 day" versus "Lexington Ground" or whatever - once it gets on that ground shipping truck, I don't think it matters a ton what your address is flagged, as it's going to go that shipping method.
The first and largest complaint people will make is that they can't use UPS Prime while on vacation or to ship gifts.
[0]https://informeddelivery.usps.com/box/pages/intro/start.acti...
I signed up for a free 1 year trial 5+ years ago, and it's still active. I don't know if they're desperate to goose their user numbers or what, but I've never heard of anyone's trial expiring.
Newegg I've found to fulfill the Shoprunner "two day" shipping promise pretty reliably. I actually get a lot of stuff the next day due to being relatively close to their Indiana drop-ship partner/warehouse/whatever.
I would love to see "independent" fulfilment centers. E.g. I order at my favorite company a few cities away, and my local fulfilment center (the former huge amazon warehose) processes it, and I get it next day. I could imagine a shipping flat, for all packages that go through "my" center. Note, I am not thinking "mom and pop" centers, I am imagining local joint ventures beween logistics/delivery companies and these huge warehouses/goods transportation centers. But still a few orders of magnitude smaller than Amazon. (For the Germans: all my Amazon packages go through Bad Hersfeld. Imagine that logistics center would be it's own company, maybe backed by DHL / Schenker / Trans-o-flex / ... I believe it has a critical size to be viable.)
Unfortunately, the free market is not going to bring me that...
https://www.ups-scs.com/logistics/warehousing.html
First I heard of this is when I found out that some "mail order" companies let UPS handle their returns. (I think it was Lands' End.)
While it is true Amazon does negotiate very good deals for themselves, they have been moving more and more into UPS/FedEx's business of shipping logistics and delivery. If these shipping companies want to survive they need to find a way to support Amazon's competitors.
Furthermore, if Fedex/UPS will start to find sucsess in this "prime" project, Amazon could instantly change it's software to add a box "only from branded manufacturer's store", or some other software change, and solve this hit and miss experience you speak of.