This is exactly what I do, and it's worked beautifully for me. (domainname)@mydomain.com is pretty standard/easy, and storing it in password manager makes it even easier.
If your Fastmail address is dfinniger@fastmail.com then you can randomly create emails like:
some-domain@dfinniger.fastmail.com
and it will automatically send them to your main email.
It's very convenient, and the cost per year is likely to be less than your hourly rate multiplied by the number of hours it'd take to set up self-hosting.