One of the problems is, to my understanding, that many people do not really understand how the EU Commission and Parliament relate to each other.
As a result, they come up with theories about how things work with "undemocratic ways" and other such misunderstandings.
In short, the Parliament is voted directly, the formation of the Commission is done with a kind of proxy (national goverments are in the loop). There is a control loop between the Parliament and the Commission; the Parliament has to OK the new Commission and if the Commission goes haywire, the Parliament can pull the plug.
As for integration, now that Great Britain is finally removing itself from the EU, we can expect more tighter structures to emerge. One of these is the European army, which has been floating around on an idea level for a long time, only to be continuously torpedoed by Great Britain. With president Trump casting serious doubts over the future of NATO and the core premise of the entire defence alliance (the idea that everyone is in it together, i.e. attack against one is an attack against all), it is only logical that Europe formulates its own pan-European defence mechanisms.
For the EU, as one of the supernational geopolitical power players, it also makes sense to tighten the co-operation on other areas, too. One of these is security. Probably one of these will be economical, and so on.