I feel confident in final choice of KEEP DOMAIN SEPERATE for various reasons. (Unless seperate regitrar triples fee after 1 year and offers no perks or meaningful dicounts).Since that's what registrars are all about this
was a good enough reason in itself.
#2 Terms of Service(TOS)with host can change at any time(Keep seperate
and have registrar lock or point to new host)giving more freedom, and
avoiding deduction cost if you don't like host.
Do the math and "free"domain for multiple years can turn out much more expensive and with less freedom in comparison.But it looks good on paper.
You can also start out on a $1.00 domain and change it later(my host said no problem)factor in free year with transfers and other perks, and seperate registration prevails.