I'm very surprised at what you are saying about SNA and BUR. I ticket at a tiny airport (CLD) that has 6 United Express flights a day. They, too, have signs up that they won't ticket during flight operations - and I accept that, as their agents are out on the tarmac loading and unloading the flights when they come and go.
I have a schedule of the flights in and out of CLD. UA Reservations has tried to tell me that they ticket all hours they are open. I know better. I look for windows of time when the plane has left for LA, and another one isn't due in for 2 hours.
They often have to call the rate desk. I was there on Saturday, during the Chicago meltdown. The agent was left on hold for 50 minutes waiting for instructions on how to reissue my paper ticket. The agent said he's heard that the rate desk is to close, and they'll have no ticketing support at all. I hope not; it is an unreasonable expectation to expect these young United Express agents to be able to handle the full range of ticket reissues without support.
It was quite interesting to see all the issues another agent handled while I was there. Several people came in to talk to a live person, rather than deal with the frustrations of the India Call Center.