Microsoft won't provide new email accounts under the hotmail.com domain
This is incorrect.
The normal "Create Account" link at https://signup.live.com/signup? allows the creation of @hotmail.com addresses:
However, you cannot use new or existing @hotmail.com addresses as aliases (once you create a new one it becomes an existing one for the purpose of aliasing):
Existing @hotmail.com, @live.com, and @msn.com addresses can't be added as aliases.
Is there a way to add an alias that is a @hotmail.com address?
No, it is not possible.
Use aliases to add email addresses to your account
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You can create up to ten new aliases per year, for an overall maximum of ten. Deleting an alias removes it from the overall count, but not the yearly limit.
Existing @hotmail.com, @live.com, and @msn.com addresses can't be added as aliases.
You can create an alias using an existing email address from other providers such as Gmail, Yahoo! Plus, or AIM Mail, as long as you haven't used the address to create a Microsoft account.
Source Use aliases to add email addresses to your account