Monthly or yearly dose is a lot less practical than weekly dose.
There are some of us who don't take the exact same dose daily - varying slightly a day or two each week, to establish a dose that works best for them. And, as you well know, our needs don't always stay constant week to week, month to month, or year to year.
If we all took the same daily dose, every day, then the weekly dose thing is of no value.
If it was possible to stay in range using the same dose every day and be in the center of the range, then weekly dose is of no value.
Alternating doses a few times a week makes accurate INR measurement inaccurate, because it changes in relationship to the doses you took a few days ago.
Personally, I take the same dose every day - and don't really look at it as a weekly dose.
When I last made a change in my dose, I dropped from 7.5 daily to 7.0 daily (requiring 1 1/2 4 mg and 1 1 mg pill).
I wonder if, for convenience, going with 6.5 or 7.25 (if it's even possible) mg/day would still keep me in range.
If warfarin users can determine a daily dose that is easy to create (in the case of my 7 mg dose, a 5 mg and a 2 mg would be easier, but I don't have 5 mg pills on hand), and still stay in range, then daily dosing would be the way to go. HOWEVER, if 7 puts a person slightly below range, and 7.5 puts them at the high end of the range, what options are there? (Yeah, a 7.25 could be made by breaking a 7.5 mg in half, adding a 2 mg, a 1 mg, and a .5 mg).
But I'm assuming that a fairly standard dosing, without jumping through hoops to get to an effective dose would keep a person in range - in which case total weekly dose would be irrelevant.