Commerce without billing address
The store address is used for calculating taxes. It doesn't have to be a physical store address, enter the address the business entity is registered to.

On the store edit form select a single "Allowed billing country".
That will hide the country selector on all of your address fields.

Then go to admin/config/people/profiles/manage/customer/fields/profile.customer.address and under "Field overrides" select "Hidden" for each field.
That will hide the other address subfields.

You need to be on the latest Commerce release for this to work.

(And yes, an empty profile with just the country code will be created for each order. There is no way around that currently)