Of course, as soon as it is seen to be a false call, the person who did the call should be arrested as that’s illegal
Proving that they weren’t genuinely concerned can be tough, and mistakenly calling the police (or emergency services in general) shouldn’t be punished or people will hesitate to call for help when they need it.
But you’re right: there should be some recourse to abuse, if not criminal then civil. Of course, a lawsuit is a lot of work and possibly money you would pay up front, and there’s no guarantee that you’d actually see much money if the perpetrator is a basement-dwelling neet whose meagre pocket money is immediately spent on Gacha games, trading cards or those weird plastic figures with oversized heads that some people go crazy over.
So maybe the state / police should instead pay compensation to the victim and, if it seems like a case of abuse, bring their own suit to potentially recover those damages from the caller. That would reduce the damage of mistakes, protect well-meaning callers from retribution and thus shift the cost for this security from the individual to the collective. It also allows an option to shift it back onto malicious individuals.
Of course, the police response could be more measured too, and the whole thing is contingent on the justice of the judicial system, but the latter part is true of any system and the former applies to many things the police do anyway.