How do I assign a true billing administrator?

Question

Good Day

I solved my problem while investigating the post as I wrote it. See questions regarding the confusion at the bottom.

I'm a global admin for my org, and I have multiple payment methods setup in Azure. Our HR person wants to be put in charge of buying office licenses, so I assigned her the following roles:

1. Billing Administrator
2. License Administrator
3. Office Administrator
4. Team Administrator

When she logs into the Office 365 portal she can see the "Admin" option in the left panel, but when she tries to buy licenses she gets:

"You need a billing account owner or billing account contributor role to buy products. You either don't have one of these roles assigned to you, or you don't have a billing account for buying products. Contact the Global Admin to get the role you need. Learn more about billing account roles."

Well I was writing this post, I solved my issue, except the logic around how this works is insane!

Why do I have to leave Azure, to grant access to something in Azure?

When I assign the "Billing Administrator" role, why doesn't that give the person access to administer the billing and charges against the account / tenant?

Why does every panel / portal have a different set of uncoordinated settings I have to play with?

If I'm using Azure and AAD, then shouldn't I have the ability to administer all roles and privileges from that point? Maybe it's ignorance on my part, or there is some excellent reason behind the complexity, but it sure doesn't make any reasonable surface sense.