I have worked in Netherlands, Belgium, Germany and France.
Belgium took 3 years to process the form for national insurance which caused me to draw down about 20,000 Euros. I couldn't drive my European vehicle in Belgium because I didn't have Belgium license plate which was required for insurance. Rather than working for the first 3months, I had to visit the gemeentehuis every alternate day to push some piece of paperwork to some government authority. I couldn't park my car in Belgium outside my property because I didn't have permission to do so because it wasn't a Belgian vehicle. In order to rent a property I needed a Belgian bank account, which I could only get if I was a Belgian resident, forcing me to live in a hotel temporarily and using that as my address. I required my accounts to be signed off by a Belgian notary, of which there is a government enforced limit, so to speak to one for a microsecond cost 1000 Euros minimum. At the time, operating a British company in Belgium cost 17,000 Euros fee. I still receive paperwork from the Belgian government more than 10 years after leaving.
The other countries aren't much better, and the only country that was easy to start working in was the UK.
Sounds like you had a bad experience. I moved to Lithuania nearly a decade ago, and my experience was just like moving to another city in my country. Opening a bank account took around an hour, they just needed my passport.
After a year I realised I should have applied for a temporary residence permit (if you have FoM you are allowed to live as a resisent for 6 months without it), which took a few weeks to get.
This year I finally changed my drivers license over, as I couldn't get a parking permit without a local license. I've owned 2 vehicles with local plates before that. Took a few days to do that.
I did the same to Ireland a decade before, and my experience there was pretty much the same.
I worked in those countries and more; never had those issues, but then again, I don't worry as much about details as you seem to do. Who reports that they are running a business in another country? The Belgians, like many others in the eu, are on paper a stickler for the rules, but in reality, not many people care or do that. Especially in Belgium where I heard locals at the chess club call them guidelines as a sort of joke.
That you need to be a resident to open a bank account is silly, I admit, but KYC and AML are a problem banks have to work with. Even in the EU, you can disappear a bit over borders: my birth country tax office lost me only after one jump and I moved 6 times since then. I always have to call them and explain things as they still don't have a clue that I am not in in my home country anymore; it's been 20+ years...
Your experience sounds a while ago; things did get somewhat easier; my gripes are opening bank accounts (but we have neobanks now; not sure if that works with rent) which should be eu wide, nummerplates (you have to import your car if you move somewhere which I do find nonsense; it's a tax thing) and renting. The rest is pretty smooth. If these things, and preferably tax, can be done eu wide, it's good. I just do the stuff I agree with and ignore the rest; it is what the locals in every country I have been to do too: hell, I am the only one (that I know of) paying (significant) taxes in my town; people laugh at me at parties.
I've lived snd worked in four different EU countries. Yes, each has some paperwork to do, but none came with the problems you describe. For the most part it was pretty easy, and anything that remained could be solved by paying someone a few hundred euros to assist with the relocation.
> In order to rent a property I needed a Belgian bank account,
This part is proper weird and (very) likely not complaint with the EU directives. All Eurozone banks must be treated the same. Since you appear to be British, that would preclude the Eurozone. Still all banks in the UK were allowed to transact in Euro although there was a spat where the guys in Brussels wanted to exclude London from the juice EU clearance.
Many years back (not in Belgium) I did get a bank account prior to obtaining the local residency. Moving to work within the EU has been absolutely hassle free for me. Again, I have not worked in Belgium.