Yeah - it's not anonymous, the shill people didn't understand the technology and are wrong.
Every transaction is part of the public ledger. If you ever want to get money in or out from fiat you need some point that is going to require ID.
You could try and avoid this doing in person and cash, but if make any mistake ever your entire history of transactions is known.
Some people have tried to do things to obscure this (coin mixing), some coins exist to do something clever to make it private, but BTC isn't and the other stuff doesn't really work.
Coinbase is great because the original exchanges like "Magic The Gathering Exchange" (Mt. Gox) were amateur hour, they were routinely hacked and lost everyone's money. Coinbase was the first real company that showed up and did what they were supposed to do. They also made things easy with good UI.
I think this is partly because in the Mt. Gox days it wasn't taken too seriously, (most) people were playing with it because they thought it was cool not because they expected it to grow in to a trillion dollar monster.
Do we know if Coinbase would cooperate with US government in such a situation? I would imagine they would.
I'd imagine they are also going to be sending IRS 1099-like forms for all crypto transactions, right?