I am an experienced telecom software engineer and I will cut to the chase about Verizon's inability to block these calls:
If Verizon is able to display "Unavailable" on your TV set or home answering machine then there is no technical reason why they can't prevent these same calls from ringing your phone if you have the "block anonymous" service enabled.
The blocking feature offered by Verizon is a complete joke and blocks almost nothing from my experience. And yes I have dialed *77,*87, *77 ad nauseam in addition to activating "Reject all Anonymous/Private calls" via my web account.
But wait!!! Verizon has a disclaimer "Anonymous Call Block rejects most phone calls from callers who have blocked the display of their telephone numbers from a Caller ID device. Anonymous Call Block will not block calls made to you from outside your local calling area or through operator assistance."
ROFLMAO, in other words it blocks nothing. Ever think a consumer might like to block all anonymous calls unconditionally? Makes you wonder where Verizon's interests are, right?
I should mention that I have the Nomorobo service applied to my account which works as advertised. Shout out to them (no affiliation) but their service is rendered useless when the caller id is "Unavailable". Shady telemarketers are catching on to this loophole thereby increasing the number of calls that slip through.
I may be able to help you with your existing "toy blocking service" and customer frustration. Free to reach out for some consultation work if you indeed care about the issue. Like I stated originally, if you are able to display "Unavailable" on my TV set or answering machine then technically you can prevent these calls from reaching my residence. I'm not actually looking for work so let me restate my position: "FIX THE PROBLEM" it's not that difficult!
Soon to be another household that says goodbye to landline (and Verizon) service!
P.S. Years of frustration here and I can see from this forum (also a joke) that Verizon has not taken any action to remedy the issue.