I don't yet have a good screen of the address on my driver license, as I get some perks where I live and want to keep that for now. I am using passport more domestically for ID because it does not have an address.
Basically, don't put any property or services in your name, and all mail uses the storefront address. I suppose rich folks have wealth management person at bank who recommends an attorney for these schemes. It wouldn't scale at reasonable price point to make a service for this, though I have considered it. Most people "don't have anything to hide" so they will not see value in such a service. If people won't opt out of TSA's voluntary full body scans, they won't be interested in privacy.
You can't screen everything overnight without help, so start small like put a car in a trust or LLC with address somewhere else.
The downside, or upside?, is that on paper you will have nothing. Definite upside is keeping controlling paperwork straight and replicated to people I trust.