It's not that the blocking doesn't work. It's that there are two *different* ways calling number info gets passed around.

ANI is far older and used for billing (collect calls and the like).

Caller ID is more recent and is passed thru different channels.

I'll note that any place that's big enough to have its own phone switch or even a sufficiently large PBX, can program it to ignore that "private" bit on the caller ID.