“Too costly and complicated....” Boom!
Each temporary visitor should have to post a bond, which would be forfeited if they fail to report leaving the country on time. The money could be used for enforcement.
It would be easy and cheap for real European’s to get a bond..it would be expensive for those at risk of flight.
It would be simple and self supporting. I know that this has been considered by the State Dept, but would be shot down by congress.