I mean, getting rid of the part of the EU executive that actually are charged with thinking of the union itself seems excessive? Especially as that would leave the European Council as the only executive, meaning it is the executive of the nations that would also have to run the union executive...

No, probably better to make the Council of the European Union a upper house of the EP and give them the nomination right, with the EUCO having some veto powers dictated by how unanimous they are.

But in any case, because the EU is a union of independent states with quite different outlook on things I think it is unavoidable that the system that endures holding it all together is pretty convoluted.