That's sadly not true, at least in Europe: since most people cannot enter legally, they have to resort to illegal way, and smuggler know this, and strangle them with bribes, extra fees etc. Most "trips" to enter through Italy for example for this reason cost thousands of dollars, not something a poverty stricken family can afford. Most economic migrants are from middle class in their own countries, who are attracted by the false promises of TV shows about how everyone in Europe or other countries depict themselves, but again, are decently well of on their own countries. Source for prices: International migration and illegal costs: Evidence from Africa-to-Europe smuggling routes - ScienceDirect https://share.google/YgcY5iFUeuZLvPmPH

For the US, on the other hand, since you have a river vs a desert + sea, can be a lot cheaper