I still fail to see the regulation inflation. It is not like there was an absence of regulation before the EU. But now once you comply with EU regulation, you have access to a significantly larger market than before, where you had to comply with national regulations.
So yeah, depending on what market your institution is from, you might see an increase in regulation. But changes are, once you expand beyond national borders, you have less regulation to deal with as compared to before the EU.
AI, RGPD/DSA/etc, yearly money laundering regs are a good example. They come on top of local regulations, they don't replace them. Each country still has its own special laws.
The original EEC was to help maintain peace through economic interdependency. Now the EU is very different with ultimate goal of full integration, i.e. a federal state. The single market is a step, the single currency is another step, EU Parliament, tax rules, now possibly defence matters, etc. Step by step but always in the same direction.
The EU started with the coal and steel initiative, which created a common market for those commodities. It was indeed "peace through trade", but mainly trade.
And the goalpost has since moved very far, I don't see really how preventing countries from sending back illegal immigrants or making same-sex marriage has anything to do with European peace.
The point made is still valid since the EEC was created in 1957 and, before it, the Coal and Steel Community in 1951. Of course it is also unclear what they had in mind with that phrasing, and perhaps it even varied depending on whom you asked: The UK government under Thatcher signed it but I think we can all agree that she wasn't aiming for a federal EU (her famous "No, no, no" speech in 1990 makes it beyond doubt). I think the people at large did not want nation states to disappear within a federal EU, either (and probably still don't).
It's still simpler to deal with EU regulations instead of dealing with the national regulations of each member country. The weaknesses of the EU are where the member countries are not aligned yet.
The problem is that it also prevents countries from reducing the regulations in order to foster local innovation, avoid disadvantageous rules (there are more lobbyists than bureaucrats in Brussels, for a reason) or adapt to a new reality (AI being a good case). Moreover, each country still have their own specific laws, the EU regs come on top, and don't decrease the amount of laws. And the EU votes a lot of laws, since its the main power it has, on average 7 per day.
Individual countries are free to scrap their own regulations that are redundant or counterproductive due to EU regulations. There are still a lot of domains that are not or under-regulated by the EU. Since that doesn't seem to happen, something on the national level is not working, and the utility of national legislation over EU legislation starts to seem doubtful.
