Easier said than done. They will start getting paid under the table or won't look for a job.

And that would make their life easier how?  How is that a likely solution for somebody in that situation?  How many people, realistically, do you think would even fall into that category?  I would guess statistically your looking at number close to 0. People don’t just go live off the grid so they dont have to pay child support.  

Or even better, undemonize abortions so that some abandoned children stop happening in the first place.

You think US is overpopulated?
Now just look at UK population and area...

True and so hard to accomplish with religion still being so important and traditional in many parts of the world.

That too, but for that all of the worlds' societies will have to change. So terrible how something as banal as sex is treated like sacrilege, something children need to be protected from, rather than taught.

Still, abortions are a very useful tool and should be as quick, cheap and normal as regular visits to the gynocologist.

Or go to the Benelux...

Yes,the center of Europe and a giant populated area.

Sometimes i feel like we live in one big city without nature spread acros different counttries and that is partly true.

That's actually not false and called a Megalocity. The Northeast Megalocity, formerly known as BosWash, is one of these urban sprawls that don't seem to end.

Btw, the one that goes through western Europe from northern Italy to the UK is nicknamed the Blue Banana and has about 130M inhabitants: https://en.wikipedia.org/wiki/Blue_Banana

I do get why somebody would think the US as overpopulated however: Most people live in big urban aeras. If you add up the Megalocities of Northeast, Great Lakes, Southern California, Texas triangle, Florida Paddle and Piedmont Atlantic, you get an urban aera of 190M inhabitants, over half the population of the US (though Great Lakes also includes some Canadian cities). The problem is that in between these large sprawls there's huge amounts of empty spaces and nothingness, which doesn't exactly exist in Europe, that pull the population per square kilometer way down the list.

What an awful idea.