As you correctly guessed, I was arguing about surveillance warrants and not physical searches. So I am to blame not only for being off-topic but also for causin

As you correctly guessed, I was arguing about surveillance warrants and not physical searches. So I am to blame not only for being off-topic but also for causing confusion by not even being clear about if. For physical searches, I agree with all your points. Searches are visible and can be questioned if invalid, so there is incentive for good (or at least acceptable) work on both sides of the warrant application. Besides, physical searches are inherently bottlenecked by manpower, so an artificial quota would not improve anything over unlimited warrantless searches, whereas a warrant requirement certainly does. In the immaterial world of modern electronic surveillance, important things change (invisibility, no natural upper bound, it having so much more utility for illegitimate use than detectable physical intrusion). I do believe that there, unbounded rubberstamping approval could easily reach a level where a blind artificial quota would be the lesser evil.