With something like Twilio I don't think you have any excuse for this part of the interaction: play a recorded greeting saying "Hiya, for fastest service, type in your account number . If you don't know your account number, hit 0 and one of our operators can help you look it up." If you get their account number, pick the appropriate CSR, bring up the details directly on their screen, forward the call and drop them straight into "Thanks for calling FooCorp. This is Melinda. To whom am I speaking please?" Hears customer name, a necessary formality because many accounts have multiple people in charge of them -- the most common situation in B2C is husband and wife. "Thanks for calling Mr. Smith. What can I help you with?" If Mr. Smith says his last order didn't ship yet, Melinda is a single keystroke away from pulling it up.

Ooh, the possibilities with Twilio make me giddy. If I can only productize one of them... (Crikey, the possibilities for per-company customization are endless. Do customers ever call you? You should be using Twilio.)