As a matter of courtesy, does one ask a provider to be a reference, or do we assume they will provide one?

Depends on the provider. I had a provider tell me after a hot session that she could be a reference for another provider. The other provider turned out to be a good match atf type for me.

Although providers are not under the same legal constraints their "reference" is much like a job or landlord reference. All that is discussed is
"Yes I saw him, he was a gentleman, he is not a problem client"

Some girls that arent professional are cut throat

They will either not answer the email-
Tell the other girl you are dangerous-

Of course, there are a good percentage, that ARE professional and will provide the reference. As us honest girls all try to look out for one anothers safety.

Yes.  Common courtesy is to get the lady's permission before using her as a reference.