I dont see the difference between a Rav sending for a different pesak when he holds the “actual din” is lechumra and skipping the Rav
First of all, if he didn’t acknowledge the other psak as legitimate, he wouldn’t send you there.
Second, if the rav would agree with you that you can skip the second rav, why is he telling you to go to him?
Every bais horaah/hotline is under a big posek, but he’s not answering every shailah – that’s why there’s a bais horaah.
And the poskim answering for the batei horaah aren’t as big, otherwise people would be calling them directly.
I’m not saying they don’t serve an important function, but they shouldn’t be for certain types of shailos.