Creating a pan-European legal entity, the right way

What would be the benefit?

Right now you can incorporate a company anywhere in the EU, where-ever is the most advantageous, and do business anywhere.

I think the same goes in the US and that does not seem to slow them down...

In the US, you actually have to register your business as a foreign entity in every state you operate in (foreign in this context means “out-of-state”) and it’s a minor annoyance, it can and does delay business.

Well, the argument is that EU start-ups are lagging because of the lack of EU-level legal entity, which is obviously not true...

In fact the best way for the EU to help start-ups is to stay out of the way as much as possible (a big ask...)

Indeed. I'd say a major annoyance. After all it includes filing taxes and sometimes you have to "align" your company name if for example you apply for federal grants.