In the UK, a service named TrueCall solved this problem very effectively for landlines. When you dial in, it checks the number from caller ID against a whitelist and if your number isn't pre-approved, you get prompted to press a number on the keypad and then say your name. The phone then rings (only if you actually pressed the number, which already stops most robo-dialler spam) and the caller is announced by name but has no opportunity to speak directly to the callee. If the callee approves, they can press a button and the call connects as normal (and optionally approves the number for coming straight through later). If the callee doesn't want to take the call, they push a different button and the caller gets to hear a prerecorded message and gets their number blocked.

This technology seems to come built into various mid-range landline phones now, and it has stopped almost 100% of junk calls since we last updated our equipment and got one of those, though it has occasionally confused legitimate callers as well and you do need to turn if off if you're genuinely expecting an automated call such as from your bank to validate something you're doing online. That's not much of a hassle though, and I don't see any reason something similar couldn't be done for mobile phones.