At least in the South of EU there are places with zero checks in place. I mean there are organizations operating in the Mediterranean whose whole purpose is to offer transport for people outside the EU without any checks required.

Honestly there isn't anything serious about such lack of checks. I'd say maybe US or Australia or such have serious checks in place -- EU is nowhere even close.

Where is evidence for very serious checks?

Sorry, you are the one making claims (which you edited a multiple times), so I won’t bother answering it more than this: you can read the immigration agencies web site for details.