Just like choosing the valve you want you can choose however you feel comfortable testing your INR. I am here in US and prefer the coag clinic. My first few tests were all over the place as I recall. I do have a non alcoholic autoimmune disease call Primary Biliary Cirrhosis(PBC) and it was pretty quiet until I had my mechanical valve surgery.
Now, with this disease flare up it also upset my INR. Pretty soon everyone was doing the dance "more, more warfarin" "less, less warfarin" and I could easily see that it had a bouncing affect on my numbers. I finally called a stop to all of it and told them I wanted to give my body a few days before we changed anything! And......not on the second day, or even the third, the gastro was getting nervous. I begged for one more day and ......wa la....came into a consistent number and dose is still the same. In the last two years I have bridged at home numerous times for tests (2 colonoscopys, liver TIPS procedure, and a surgery for a kidney stone that had miraculously vanished?!) At last cardio visit all is well.
So the choice is yours either way. Oh....and today when I had my INR done they hand me a sheet of paper, I get the test done just about anywhere in the USA and fax it to coag clinic and they will inform me of any dose change. They had a huge stack of papers as a LOT of people travel and it is a misconception that this is not easily done.
We do not need to get into discussions about health care systems because it just does not matter as long as you are comfortable with YOUR choice of how you handle it. I leave it to the professionals as that is what they get paid the big bucks for.