That is indeed the goal of implementing the blockchain technology- eliminating the need for a third-party trust system while relying on decentralized system wherein it is monitored publicly in a legder. But storing our password in our private keys has also the disadvantage of getting hacked due to its nature being accessible online. I guess it is advisable to not input your password online.
I wouldn't say that blockchain is the perfect solution but I guess that blockchain could help solve the problem of anonimity. Being anonymous online is what Satoshi Nakamoto wants for all of us and we are all embracing it right now. And you're also right that we can store our own ID and pass in blockchain so we don't need to rely on the government.
The anonymity factor that cryptocurrencies possess is a double-edged sword. It can be both beneficial and destructive at the same time depending on who is exercising it. That is also the reason on why the government prohibits the massive implementation of such since they fear that it might spiral out of control by means of purchasing illegal things.