Compartmentalization like this also allows some influence to spread more than it would in a unified information space. It's possible for a larger country to convince a smaller one to side with them on an EU level issue, while "paying" for it on a national level.
I think that because of these barriers it makes sense that a lot of European voters feel entirely disconnected from EU level politics. It's preteen met with an attitude of "Brussels decided that we must jump, so we jump." It's reminiscent of the Soviet times with "Moscow decided". (Not in the decisions itself, but people's attitudes.)