The problem there is the "national imperative" part imho. All EU politicians are hell-bent on ignoring any kind of market-based solutions, doing everything through regulations and picking winners. So there will never be a proper market equilibrium and therefore prices will always be higher than in places without all those regulatory interventions.

Investment won't help there in any way, because if that investment were worth it, it would already happen because of market forces. If it doesn't happen on its own, then the state (doesn't matter which level) has to do it, which means using tax money, which means that prices will rise. So that state investment will further skew the market equilibrium, putting the EU further behind.

I am not sure I understand what you are trying to say. There is currently a lot of demand for building out solar and wind in Germany. There is also large demand for building battery storage. The demand especially for the latter comes from the mismatch between supply and demand in electricity markets, so in a sense the battery operators hope to do arbitrage in a way that will also increase the efficiency of the market (by allowing the use of solar after dark).

This is very much a market-based solution. What the state has to do is provide permits and stuff for getting the batteries etc. actually built; which the state is doing but not as fast as it could right now. (at least in Germany)

Also all the regulations are based on hardcore ideologies. EU truly wants to be carbon neutral and that is applaudable, but at what cost is the question. Does is make sense to decimate most of the energy heavy industries in the continent to be carbon neutral? I guess only time will tell.