I researched them in the past but couldn't find any public list of the banks they support, so it's hard to tell how much coverage they have compared to Yodlee.com for instance.

Do you have to be a paying customer to pry that information (i.e. list of banks they support) out of them?

No need to sign up. You can actually find the full list in our docs: https://plaid.com/docs/#long-tail-institutions

Not correct - I had to sign up for an account just now so I could get API keys to hit the endpoint.

Besides, the account is limited at the moment. I get the following error:

    {
      "code": 1306,
      "message": "invalid institution permissions",
      "resolve": "Your Client ID does not have access to this institution endpoint"
    }