As someone who was recently injured and waited three months to see a specialist in Seattle, these lines were not helpful ("yes, you should make an appointment"). The only way I was able to see someone was to write a script that blew up my phone when I got a cancellation window email (the first two I missed even though I responded within 30 seconds).
Yeah, those lines are for triage, not specialty care. It's nice when you've got an infant and are a new parent and everything is terrifying, or a fever and want to know if it is bad enough to warrant going in somewhere.