Do warrants really make that much of a difference? I don't really see anything that could be considered incentive or control for keeping that mechanism from slowly (or not slowly at all) degenerating into a rubberstamping process.
I could easily imagine a system that leaves case by case decisions completely to law enforcement practitioners, but constrains them with paper trail requirements (accountability, I do agree with that part) and, most importantly but unfortunately kind of irreconcilable with the legal mindset, an artificial quota that forces them to actually think about the case. I believe that a system like that might in the end lead to less frivolous eavesdropping than one where everything is fair game as soon as they get someone authorized to sign off a form. "I got it signed off" goes a long way when it comes to questions of moral licencing: suddenly it becomes someone else's job to feel bad about it if maybe someone should.
As in motivated law enforcement would want to avoid a questionable warrant that could ruin all their other achievements related to the case? Certainly not in Germany, where the admissibility of evidence is not really a factor: if evidence is assumed to be true then it exists no matter the provenance, if you want to sue the obtaining party for the obtainment process that's a separate case.
And what about situations where the surveillance doesn't even result in a trial? If a suspicion is made up to gain e.g. intelligence over some personal opponent (or personal opponent of someone the eavesdropper swaps favors with) evidence disadmittance couldn't even be an issue at all. But the party requesting the warrant would find it comparatively easy to appease their conscience with "nothing I wrote in the warrant request was a lie". I believe that most people doing bad things don't really like to acknowledge that to themselves, and that many who might actually talk themselves into requesting a questionable warrant would rather not risk running out of "wiretap wildcards" they might later need for doing their actual job. Of course a system trying to cause self-regulation with a quota could still be designed in dysfunctional ways (e.g. if there were "leftover wildcards" at the end of a quarter, those would be powerful fuel for abuse), but with a bit of care those pitfalls should be avoidable.
at least in the States one effective counterforce to this concern is that judges are very adamant about the separation of policy making (legislation) and the courts (judiciary). Most judges are conservative (read 'purist') about the doctrine of the separation of the branches of government and don't take well to pressures from the other two. The upshot is that warrant issuance is seen as a vital part of their domain and they don't sell it away.
I could easily imagine a system that leaves case by case decisions completely to law enforcement practitioners, but constrains them with paper trail requirements (accountability, I do agree with that part) and, most importantly but unfortunately kind of irreconcilable with the legal mindset, an artificial quota that forces them to actually think about the case. I believe that a system like that might in the end lead to less frivolous eavesdropping than one where everything is fair game as soon as they get someone authorized to sign off a form. "I got it signed off" goes a long way when it comes to questions of moral licencing: suddenly it becomes someone else's job to feel bad about it if maybe someone should.