Registering a company remotely should work. That's the easy part for Estonia to implement because the company registry is a government office.

Opening a bank account is more difficult because it's up to individual banks to make the decision to allow remote account holders. Banks are private companies, and government can't easily force their hand without the big hammer of passing some legislation in the Estonian parliament (which would then also need to be vetted for compatibility with pre-existing EU law).

In my experience, European banks seem to go out of their way to make it difficult to open an account. I've had bank accounts in Finland, France and USA, and the last one was a breeze compared to the others.