Then provide an alternative solution MSH. By all means, the floor is yours.
Well then:
Full funding and temp hires for USCIS.
Relegate HomeSec to a contributory instead of oversight role, consider establishment of a full department for immigration and emigration (it needs it).
Match yearly immigration quota to percentile growth or shrinkage of immigrants arriving.
End the war on drugs and offer Mexico the assistance of the armed forces in breaking cartel and jackal activity.
Offer green cards to Canadians who graduate college in the United States.
Amnesty for existing illegal immigrants who have not committed a violent crime.
Prosecute employers of illegal immigrants and have them charged back-pay.
Expand green card lottery to make engagement with the system plausible.
Engagement is the ultimate goal here. Fact is, no system stops border crossings based on harshness. People pass the NK-China border as well as the NK-SK border illegally all the time. People passed the Berlin wall. So even if someone went all the way to the extremist conclusion that some politicians might actually support and started shooting at people approaching the border, it would still fail. There isn't enough manpower available to genuinely guard the US-Mexico border, and the costs would be too great in money and lives.
Rather, illegal immigration is prevented by compelling compliance to the system. This requires a system which people consider reasonably passable, which the current system really is not. And so they sacrifice other things to get inside the US and then hide for the rest of their lives.
None of this would be happening if not for funding-phobic hardasses letting USCIS go dysfunctional.