I've found a good way (I think) to handle those Customer Care Representatives who put you on hold while they, "put you through to the right person".
Call the Customer Care number and hit the button for whatever they call the real, live person who will speak to you. Get his/her name and make a big issue of writing the name down. Ask if there's any way to contact him/her directly (there usually isn't but this is all preliminary to the real drama).
The real drama:
State that you have a problem. That you have called earlier and it hasn't been solved (don't worry, you can lie your arse off - what do you think Customer Care Reps do?). Then state that you will not wait for the right person to be put on line.
Of course, you know Pushkar / Mina / Tina / Connor / Jackie / Whoever is just the point of contact. Reassure him/her that you know that, then hit the action button.
Action Button: "I don't want to talk to the person concerned. You do it and solve my problem."
(S)he will protest. Will tell you that, unless (s)he puts you through to the person concerned, your problem won't be solved.
Calmly say that, unless the problem IS solved, you're switching to another provider. And that you don't want to talk to anyone else. In fact, being put on to anyone else, in your opinion, is evidence that XYZ doesn't want to solve your problem.
Then ask him/her to get a piece of paper and write down your exact problem. (It helps if you write down the problem beforehand). Dictate your problem.
Then tell him/her that, unless the problem is solved within the next 24 hours, you're switching.
Don't accept any plea that all he/she is a facilitator. Tell him/her to facilitate a solution.