Banks and some other entities have databases of these services. Some will not accept these addresses. They will let you use them for mail, but they will also require a physical address and proof that you live there. But others will not. It depends on which mailing service you use and which bank, etc. This is my personal experience.
Recently, when I (in Australia) opened a US investment account, the US firm I was using wanted to see a utility bill to prove I actually lived at my home address. I ended up sending them a copy of my water bill, which they accepted.
However, if a person owns multiple residences, all that proves is that you own that residence, not that you actually live there at all. At least in my jurisdiction, landlords receive and pay water bills (and the tenant has to reimburse the landlord the usage portion of the bill), so a water bill could even be from an investment property one is renting out.
With electronic billing, you can have a billing address that doesn't actually get a bill sent to it. So if you have something that doesn't require the actual physical address (like a cell phone), you can use that as your utility bill, and no mail actually shows up.
That's why cell phones bill aren't accepted as utility bills, for many cases. Electric, water, sewer -- these things have a physical connection, and that's what they want to see.