Not most of EU but geographically large and diverse and low-latitude countries will. Spain has winds from three different sea areas and is known sunny, so they are in a good position.
Well that' doesn't always scan. Austria has a lot of wind, sun and hydro so its energy prices should be in line with Sweden, Norway, Denmark amongst the cheapest in Europe, and yet it's routinely amongst the more expensive in the EU.
Trading across borders seems to be a part of this story.
If your local price is high you can import, if it's low you can export.
If you're at the end of a grid and/or your transmission capacity is limited your price has the possibility to go higher or lower without that damping mechanism.
Electricitymaps has a pricing layer which seems to show central Europe moving in sync when I randomly check it:
And the counter intuitive thing is that people in countries with lots of renewables and not so many external links (e.g. Scandinavia with hydro) might be against adding more links since it will increase electricity prices.
So energy in Spain is cheap because they produce a lot but can't sell a lot easily, and Austria/Central Europe is expensive because they sell their domestic energy too easily?
If this is what you meant, then it sounds like an argument against free trade, if it means you keep ending up with the short stick.
Free trade doesn't always benefit everyone equally, only a net benefit overall. It's a bit like how people often misinterpret the second law of thermodynamics "but the entropy decreased when the ice froze!"
I checked and it looks like ETS are increasing prices of gas produced electricity 20-30€/MWh.
So not little (although peaks are around 140€/MWh).
But these are taxes that can be used to reduce the reliance on gas (actually, it's mandatory to use them for transition projects).
Austria could be there but they would need to build oversupply of solar, wind and (pumped) hydro to saturate the export grid lines. And currently Austria isn't building renewables at scale. I think there is a strong NIMBY movement so the best places to build wind and pumped hydro are blocked...