There are mail services that do this - it's like a PO box, but not provided by the postal service and they will forward your mail to anywhere. These services are quite popular with RV folks and world sailors. Some will even scan your mail for you.
A 302 is like a letter that's been marked return to sender with a forwarding address. The original sender would then know the actual physical address.
First your mail is routed to the provider’s local address or central warehouse, then they manually forward it to you. Some providers (incl the popular Earth Class Mail) operate as a hub-and-spoke network: all mail goes to their centralised distribution center, they process it and send it to you. This means if I buy something from a few blocks away, it will first have to Midwest then back to me.
I’m okay with latency and eventual consistency. I just need an analog->digital funnel for paper mail when I’m thousands of miles from home.
The main discovery was how much of the "virtual address" industry is a nice wrapper around two independent service providers I call "processors" and "sellers".
"Processors" are the people who actually handle your mail. Often they are existing businesses like serviced offices, co-working places, pack&ship outlets etc. These small businesses have a fixed address and personnel, so their marginal cost of handling envelopes is much lower than having to sustain an office dedicated to processing mail. These processors are combined into a whitelisted network and this is how you get many addresses everywhere.
"Sellers" are the endless firms that sell access to networks of processors at arbitrary prices. There are exceptions (e.g. EarthClassMail) who manage their own processing, but most companies I found on the internet are just billing fronts with an app. I found this out because I kept seeing the same "virtual addresses" all the time, so I inspected those buildings on Google Maps or in person.
My selection criteria had three parts: 1. Deliverability (can I send both letters and packages, and will they arrive?) 2. Longevity (will this address exist tomorrow?) and 3. Security (who might be looking through my documents?). Based on this criteria, I have almost no regard for who the "seller" is, and it's all entirely about the "processor". By reviewing addresses given, I found out that sometimes the "virtual address" belongs to a shipping/mailing outlet. These people are dedicated to mail, and tend to be very stable - I prefer them over services offices/co-working places that have other priorities. I also found some mailing stores that were actually UPS stores, and I see this as reducing the risk further.
So for ~$30/mo, all my snail mail goes to a UPS store (managed by the seller service at https://www.anytimemailbox.com). When new item arrives, UPS people send a photo of the outside and I decide whether to trash or forward the item (or pick it up myself). This address looks like a regular apartment number (e.g. "123 Main St #45") and I can use it everywhere (unlike a PO box). In fact, it is listed as my primary address with the phone company, the bank, state driving license, insurance company, government records, and all business registrations. I try to be paperless, but now I am free to travel or move as much as I want knowing I'll never miss anything important from the old school of correspondence.