Just for my own epistemic hygiene, would you mind clarifying your familiarity with applying for and receiving a similar warrant and the duration you envision when you say "wouldn't take a long time"?

Very reasonable not to, of course, but it helps me adjust my understanding of things. And yes, if a warrant is a 10 min process at p95 from call receipt to warrant acceptance then that certainly allows for things like "this car was stolen in an armed robbery 20 mins ago; we'd like to track it through the city" without too much concern, and I would switch to requiring such an SLA[0] on warrants combined with a requirement on warrants that can be rescinded if the SLA is violated.

0: strictly nonsensical here, but I think you get the picture