Full disclosure I am overly critical and often times don't see the future use of technology/apps - I think I told Diggity 20 years ago that I didn't see Youtube and low res videos taking off.
That being said..., a few scattershot points:
1) Consumers don't care who you have to pay. The why isn't important to them, only the $$$ is.
2) Is this a call screening service, an anti-spoofing app, or both? If it's a screening service, can you charge less than a person in the Phillipines I can pay $5 to screen?
3) You seem to be promoting it as a "make $1000 going after these guys -- we'll do the legwork", but then seem to imply that 99% of the value of the app will be in anti-spam. If it's the latter, you are going to be very hard-pressed to find anyone willing to pay a subscription fee and just hope your product works better than the free products.
4) What do you think the monthly $$$ value of your app is to a non-business user? As mentioned before, business users can get a virtual screener/secretary for cheap (that also handles a lot of other tasks), so if your target is the regular Joe... at this point how many regular Joe's are picking up the phone if it's a number they don't know?
5) If you do prove that consumers are willing to pay, what will keep the service providers from offering their own service for free?
6) Would customers be constantly updated on the legal status of their cases for each and every number? Would they just have to trust that if there's eventually a winner in there that you'll let them know? If you actually are able to get funds? A year+ later? It's a nice carrot on a stick to get people onboard, but the carrot is a lottery ticket at best it sounds like.
7) I think what it boils down to is that it's a major problem, but it's also simply an annoyance -- and people aren't going to pay $60 a year to maybe have that annoyance lessened but likely not eradicated... They'll wait until some kind of legislation forces the carriers to do so - which I have to assume is coming - as with anything it's just gonna take a Congressman to get his number spoofed and embarrassed somehow. So to go along with #6 above, the consumer has to hope the company pays out AND is not rendered obsolete over the course of a year.
With the increase in data breaches and identify fraud, giving a new company complete access to your phone and every single incoming call with just the hope that it will lessen an annoyance... and having to pay for it to boot? Just doesn't seem like it would have enough signups for any consumer to have confidence that they'll actually have a chance at a lottery ticket, much less get the money from one.
I'd say unless you are free, or free with ads, you won't get enough signups.