Yes, and also, as toast0 says, it's likely to be impossible to have all those providers agree on such a system.

But phone operators should do something, like block voicemails left by a robot, either by detecting them automatically, or blacklisting numbers, or, why not, offer the option of a captcha before leaving a message:

in order to leave a message to this person, please enter the result of the following operation: how much is 3 times 4...

Maybe there's an opportunity for a startup here. It could work before the fact with a captcha as above, or after the fact: it would listen to your messages and spam-rate them.