I don't know about living in Europe illegally, but I can tell you that I at one point considered moving to Germany legally (and was offered a job there, which is very much a prerequisite for such a move).

I have found their immigration process so onerous, I decided against it. One of the most irritating things was, my wife would not be able to work for 5 years (IIRC, it's been a while) if there are _any_ Germans whatsoever willing to take the job she'd be applying for. She's an accountant, so that would definitely be the case. I mean, I see the point of all this _for Germany_, but that definitely put them at a disadvantage in attracting me to work there, in addition to much lower pay that my profession gets in Germany (which, ironically made the second income much more desirable).

People in the US seem to think that EU is this open borders paradise where "ihre papiere bitte" is not a thing. It very much is a thing.