Legalize those who are illegal but pay taxes, don't have a criminal record and have more than 10 years in the country

Most people agree that the majority of illegal immigrants contribute to the country's economy.
Think about it: No more hit and runs because the person is afraid of staying to report the accident to the police, no more people applying for benefits with fake names / documents, etc.
They all would love to go visit their countries, which would help their and our economy! They would travel within the US! They would purchase houses! They would purchase better cars!
Why? Because they don't have to be afraid of deportation! They are certain that they can stay here, which makes them responsible for their bills, taxes, etc.
Most important: FBI verifies their records when they apply for a petition, therefore ZERO to VERY LITTLE chance of a terrorist becoming an American.
So, why not?