Katie, if the ISBN isn't registered to you then you often don't have access to the various storefronts you refer to, as only the publisher of record can control those. And the publisher of record is the person or publisher the ISBN is registered to.
I'm sorry, but that's just not correct.

Amazon/KDP, B&N/PubIt, Kobo, All Romance, and Itunes do not require an ISBN. You upload directly and they use their own internal identifier.

Apple has irritating issues, including requiring a Mac to upload and listing your legal name as publisher if you don't have a DBA bank account to deposit to. B&N/Pubit doesn't allow non-US based accounts. Smashwords and Lulu provide access to these stores and take 10%. You can waste money for a vanity ISBN or use the free ones registered to them, but it's really irrelevant. They still take 10% and you still manage them through exactly the same control panels.

Createspace and Lulu both do POD services. You can waste money on your own vanity ISBN or you can list them as publisher, but it's essentially irrelevant. Most sales will still come online. Even if bookstores did stock your books, they'd be ordering them from CS or LL, not from you. Like using Smash/Lulu, the experience and financials are identical no matter who's name the ISBN is in.

The only real purpose of an ISBN that I can is for you to print your own books, stick them in the basement, and wait for bookstores to order from you. That's something so rare as to be irrelevant in modern "self publishing." (It's also the fantasy that the S&S vanity press Archway really heavily pushes.)

You could, I suppose, declare that nobody using Smashwords or Createspace is a "self-publisher," but seems a little farfetched.