Sorry for the delay in getting back to your post YOP, I've been on duty for the past 4 hours and in the air for 3 of them. Only just on my third brew now
If you want something more interesting then join the crew on the air ambulances who get results every day and do not come on here moaning.
Wow, that's one huge assumption on all of those points you've made there YOP! Having done that job, I know which one I prefer

You have just proved that assumption
is the mother of all ****-ups
Looking at the numbers a typical UK police pilot is going to spend most of his working week sitting on the ground. That is the nature of the job just like a dog handler.
And exactly the same 'nature of the job' for one of your beloved air ambulance pilots. I'd like to see your air ambulance/police pilot flying time figures. (See the first line of this post) I'd also really love to see where you got your dog handler information from, but probably not as much as a dog handler would
Most of your work will involve petty crime and missing persons who usually turn out to be not missing.
IMHO, The only 'petty crime' is the one that happens to someone else! Ever hear the phrase, from little acorns might oak trees grow? Much the same for 'petty crimes', they tend to lead elsewhere!
Just because a police ac gets deployed to a misper job, doesn't necessarily mean that we expect to neccesarily find that person. Surely the main unquantifiable part of all of these searches is being able to clear vast areas quickly, enabling the officers on the ground to follow other leads of enquiry ultimately leading to the successful location of that person, instead of that time being spent on the massively time consuming ground searches. It also allows those units to clear and be despatched on other jobs. (The thin blue line is unbelievably thin!) And for your info, we do actually end up finding some of these missing people, usually in locations where ground officers wouldn't.