You do see the inherent contradiction in your statement, don't you? By definition, illegal aliens aren't law-abiding.
Law-abiding foreigners by definition can only include those who enter the country legally.
If you make it easier to enter legally, fewer will go to the trouble to enter illegally. If you make it easier to stay legally, fewer will stay illegally.
A retired Brit, may enter the country as a tourist, but stay and buy a house in Florida. After his tourist visa expires, even though he has applied for permanent residency, he is staying here illegally. The system is so slow that he may die before he gets his green card.
There is no reason for the delay. Sports stars can be recruited and get their visas in a matter of days. But if you’re recruiting a paralegal with Portuguese language abilities, be prepared to wait.