It would be nice if the world would all fit into prospective, double blind, randomized clinical trials, but it doesn't. Some clinical questions are difficult or impossible to study in that manner. Soetimes even case comparisons are not practical, particularly with relatively rare conditions. So we have to resort to extrapolation of principles derived from other clinical scenarios. It is imperative, of course, if we wish to call it science, that the principles be placed in the context of a scientific theory, whose objects are derived from observations.
Anticoagulation can reduce the extent of propagation of clot, even in the presence of stagnat flow.
When clots mature they adhere and become less likely to propagate or embolize. There is histologic evidence on autopsy studies that thrombus formation and propagation is an important mechanism in myocardial infarction. I would, in fact, ask you establish that by studies before refuting the extrapolations that I have suggested. I am pretty sure that a review of blunt carotid injuries will show a general concensus that full anticoagulation is the accepted treatment of choice. I grant that this is based somwhat on assumptions and would like to see comparative data, but it would be tough to get.