A few definitions and other info:
Warfarin is the generic for coumadin. When coumadin was protected by patent, it cost about $1 or so a pill. You can get the generic warfarin - which has been proven to be biologically equivalent to coumadin - for about a dime a pill.
Warfarin does not THIN blood. It extends the time that the blood takes to clot. The use of warfarin is to minimize the risk of a clot forming on or around the valve (or inside the aorta in the case of aortic fibrillation).
Although there are guidelines for target ranges for INR (international normalized ratio - a basis for evaluating prothrombin time), dropping below the range, briefly, isn't necessarily the death sentence that some people seem to believe. (I've fallen down to 1.2, after some antibiotics and other non-prescription medications that seemed to make my INR drop, and increased my dosage, watching the INR go back up).
Self-testing is a GREAT thing - it enables you to test as frequently as your clinic schedules it, or as frequently as you're comfortable with it. Instead of paying $50 or more for a lab to do the test (and, as a result of the cost and inconvenience, tests are often scheduled weeks apart), you can do it at home for a few dollars.
Some of us even feel comfortable enough to manage their own INRs. (My drop to 1.2 happened when I went 10 days between tests, instead of my usual seven days -- it was relatively simple to bring my INR back up).
I don't think that warfarin should be feared as much as it is. Your blood just takes longer to clot. As long as the INR isn't TOO high, it's really not much of a problem.
(I've had a concussion, and there was concern about a brain bleed, and I've dropped a heavy chunk of marble on my foot and got some massive bruising, but these things are atypical - even for me).
There has been talk about work on new anticoagulants. There's talk about them coming out within the next decade or so. I even talked to a meter manufacturer who was concerned that the meters may not be needed at some time in the future.
HOWEVER - a new medication will probably cost many dollars a day. It may have side effects or other related precautions. It probably WON'T be perfect. Compared to the dime a day for warfarin and weekly (or so) testing, it may be worth the inconvenience of testing to avoid the high cost of a possibly superior medication.
What may be good for future generations needing new valves would be a mechanical that reduces the risk of clot formation -- possibly requiring only an 81 mg aspirin - or less - to prevent clots. THIS would be better than a new pill that costs many dollars a day and with a patent that will probably keep us paying way too much for decades.