Very much this.
Plot twist: Genghis Khan is reborn in Finngolia and uses the EU army to conquer the world, shore to shore, ushering in the new age of humanity. London is turned into a post-modern tower of skulls for rebelling
If the EU actually morphed into a federal governing body, do you think there would be more incentive to make the EU parliament more democratic?
Short answer: No
Long answer: No, because there exists no incentive for EU ministers to do anything but centralise the European Union. Making the EU even less accountable merely further removes them from the people they rule. If we look at the EU's past, even when member states were being forced by their electorates into halting EU integration without consultation, the EU responded by proposing further centralisation. Even when the UK was likely to leave the EU, the EU responded by promising further centralisation. Even when softer eurosceptics in other countries called for
slower integration, not even a halt, the EU responded with promises of further centralisation. After the UK voted to leave, the EU responded to this crisis caused by resentment to EU centralisation by promising accelerated centralisation. Allowing the EU parliament to actually do anything would run the risk of allowing european voters to disagree with the EU, repealing and reversing EU laws & centralisation. It is a political entity you join and are never supposed to leave, the EU only centralises, it never relaxes its grip.
Centralising more power at the top, giving less accountability to anyone - the last thing on their minds is going to be devolving power when the objective is inherently about centralising European power under one polity. It would be like the United States of America's federal government forming in order to make every constituent state sovereign, the concept is inherently self-defeating. With as much money and power as is concerned with the European continent, it'd look like the American federal government's worse qualities on steroids translated through google 27 times
I ask because through my american viewpoint, the EU would feplace the national governing bodies as the highest law of the geographic area. Now, as the representatives for those bodies are elected, in a general speaking, would this tradition then transition to the new governing body?
Yes, I know they wouldn't want to hand over appointing power to the voters.
This one requires a bit of nuance to explain, since all of the European nations have their own democratic and constitutional ways of electing their leader, as a consequence it is unlikely that any one system would be imported into EU-level governance. The most likely outcome to result in a relation between voters and the Presidency of the EU would be the European Parliament electing President of the Commission from amongst their ranks, with the European Council becoming vestigial/ceremonial in its selection of whoever has the Parliament's confidence. The other thing it would need is the ability to propose, amend & repeal legislation, and you'd have something which would begin to resemble a Europe-wide parliament.