If ther parliament has no initiative right for legislation, there is no directly democratically legitimized legislative body. And the EU comission is way to indirect to be considered properly legitimized.

That the US is lackluster in its criminal system should not be an acceptable example for us.

While your citizenship extends to allowing you freedom in other EU countries there is still plenty differences outside the EU. But you wouldnt find it that inside a nation state people from one federal state can travel under different rules than people from another federal state. They are all subject to the same rules and that needs to be the case for the EU too, to achieve statehood.

With the unified administrative system it is not about control from one place. It is about uniform standards and uniform interactions. For instance getting married requires different papers and prerequisites depending on country. Things that are a complicated act with multiple personal appointments in Germany can be done in 5 minutes digitally in other countries. This is unacceptable for a nation state.

we do not really have eu wide political parties yet. there is alliances, but those are different and people can only vote the local part of the EU election. There is no EU wide electable lists and worst of all there is different rules to the countries EU elections. Something again impossible in a true collective nation state as elections need to be equal.

So we are still a long way from having the EU works as one nation state.