BTC Wallet's

Do they all now require ID as in terms of last four digits of SSN

Not really, software and hardware wallets.. even some websites require nothing

One of the big points of Cryptocurrency is that its almost anonymous. Of course you can still have your real life "profile" attached to your bitcoin address, but if you are careful, this will never happen.

The only wallets that require your details, are wallets where you are purchasing bitcoin using fiat (real life money). Just regular bitcoin wallets do no require a verification. I recommend using https://www.blockchain.com/ as your bitcoin wallet if you aren't in the market for a hardware wallet.