It's possible in the US, but it's getting very difficult. I don't know anywhere you can buy or or borrow a DID with Monero anymore. Looks like they got to Telnum recently.
You can still buy a SIM, a prepaid PIN, and a phone with cash, but you'd need to pay a non-correlated person to be seen on CCTV to do it, at a non-correlated time, and hope they don't just take your money and leave you nothing at the dead drop.
Then there's the hassle of setting up the account in a way that's not correlated with your location, normal waking hours, etc.
All of this could just be avoided if Signal did the right thing.