The threat of asset seizure of property owned by illegal aliens would do wonders.
It won’t get the thousands who game the welfare system to leave, but it will remove a big incentive for a lot of illegals.
Asset seizure involves police powers and court system. Timely and expensive. Great idea, but costly and time consuming.
Issuing an EO and using the tax code to give business owners the profit motive to fire illegals is much quicker and doesn’t cost the government much money to implement.
You frame things as an either/or choice when, in fact, multiple options can be done in parallel. Go ahead and build a border wall, hire more guards, and do asset forfeitures. The more policies the merrier!