I've had a wide range of responses from people calling me when I tell them I won't give personal details out based on a cold call.
A few understand immediately and are good about it. Most have absolutely no idea why I would even be bothered about an unexpected caller asking me for personal information. A few are practically hostile about it.
None, to date, have worked for a company that has a process established for safely establishing identity of the person they're calling. None. Lengthy on-hold queues, a different person with no context, or a process that can't be suspended and resumed so the person answering the phone has no idea why I got a call in the first place.
(Yet I'll frequently get email full of information that wouldn't be given out over the phone, unencrypted, unsigned, and without any verification that the person reading it is really me.)
The organisational change required here is with the callers rather than the callees, and since it's completely about protecting the consumer rather than the vendor, it's a change that's unlikely to happen without regulation.