It will be regulated.
The government already tracks down people through the blockchain.
If you only ever stayed in the blockchain and only sent transactions P2P you will still be found.
Most people have to put cash from their bank or from somewhere into their wallet address, which creates that link. You have to be a true fool to think Bitcoin is truely anonymous. Nothing over the internet will ever be truely anonymous, everything can/will be cracked, everything is hackable, everything has flaws and always always will. Nothing in this world has ever been perfect ever.
When you look at this from a perspective of history + reality, then you already have the answer to your question. It will be regulated because all governments create regulations on everything and always will.