The solution is simple: patrol the border itself. Anyone that gets through, gets through.
Make it extremely expensive and/or unpleasant to get caught employing illegals, and increase avenues for legal immigration. Same goes for public assistance — none provided, other than a truck trip to the nearest border, if a non-citizen finds themselves in need of going on the dole. Anchor babies go with them — they can come back when they’re 18. The problem will all but disappear if there’s no economic incentive for people to jump the fence.
Oh, and end the war on drugs tomorrow. No need to harass people looking for substances if said substances are legal.
The other option is to take NAFTA to its logical conclusion and have a full border and employment rights union with Canada and Mexico.
Lastly, just because it stops crime doesn’t mean that it’s right, nor that I (or any other American) have to like it or shouldn’t complain about it.
PS – how do you know the increased questioning wasn’t random? Most cars got waved through. Some didn’t. Do you know that they weren’t stopping say one in twelve cars for further scrutiny?