I worked (briefly) on the switchboard at the BBC (in 1997) so got to see the other end of this. Complaints were actually taken by a separate department, but that didn’t stop people calling asking to speak to “a producer please” and venting at you when you asked them to be more specific/ told them you could only put them through to the complaints department.
I once had Mary Whitehouse on the phone to me
When Star Trek was delayed due to the Tennis over running, or a film showed an animal being hurt (think it was a dog in a JCVD film) the switchboard would light up like crazy