It would be nice if there were some way to penalize the person wasting the cop's (and your) time. As with spam, it's easy to do because the cost is zero.
That's just the first three nodes of a N>10^8 causal graph.
Wasting police time is an issue, yes. It would be even more of a waste of time trying to establish whether this person had reasonable cause to call the police or was just trolling. Not to mention the other consequences I touch on above.
Suppose you want to incentivize people to report if they are at least 5% confident that there is a problem.
If you choose some small cost (say, $5 for example) if one is wrong, then if you assign a reward which is at least 19 times the cost if one is wrong, then the expected monetary value of reporting (in addition to the benefit from/of being altruistic) is positive when one is at least 5% confident that there is a problem.
(The ratio, where p is the minimum level of confidence you want people to report if they have, between the cost and reward, is (1-p)/p .)
One might question whether creating a monetary incentive scheme like this would still cause problems (akin to the expiraments about kids being monetarily rewarded for quality of artwork in schools decreases motivation or something like that), and that does seem like something that could be the case,
But one can set up a system that doesn't just disincentivize reporting when one has any doubt (as a simple fine for false reports would do), but still disince tivizes sufficiently uncertain reports.
That doesn't mean it would be a good idea though. I don't know if it would be.
The real problem lies in the numbers: To put it simply, the cost (salaries + funding) to research this issue and evaluate a good scheme and then implement it could be much higher than several years' worth of "noisy" police calls. Add this up with the opportunity costs (what those thinkers/researchers aren't doing while they're busy with this) and it's probably all the way down to "Will Do This Only If My Next Election Depends On It".
I've had someone call the cops on me because my son had a meltdown. I'm white so I just had a nice conversation with the cop, and I didn't get shot. But there are certainly people for whom even a random encounter with the cops has a good chance of turning out very badly.