That sounds like it'd require a huge overhaul to the phone system. At which point... why do the telcos even need to be involved here? VoIP is common enough now

That sounds like it'd require a huge overhaul to the phone system. At which point... why do the telcos even need to be involved here? VoIP is common enough now that you could just have a menu system before the call and trigger a VoIP call to the right department automatically. And heck, let's get rid of phone queues while we're at it - just have the agent trigger a callback rather than making them listen to an awful hold music loop for potentially upwards of 15 minutes.