Thank you for the question @MikeLandau, and sorry for taking a long time to answer - I was hoping someone from the biomedical team might respond, but I can give it a shot in the meantime anyway!
As far as I understand it, vascular dementia could be caused by a range of conditions involving impaired blood flow in the brain. So even if stalls could also be one of the contributing factors, it might occur only in a small subset of cases (others resulting from stroke, deterioration of blood vessels etc., or blood vessels clogged in a different way, but not necessarily stalls). In that case, a drug that helps to reduce stalls in the brain (i.e. reduces the amount of leukocytes stuck to capillary walls in one way or another) would probably benefit only that small subset of vascular dementia cases. Additionally, it is possible that the drug could induce other unwanted effects that might not affect an Alzheimer's patient as much, but could do so in vascular dementia - depending on that drug's mode of action. In general, it would be very dangerous to even test a drug without knowing the molecular mechanisms behind the disease & where in the molecular pathways will the drug interact, and what other processes it might influence. (Even though such trials do happen sometimes anyway, I guess.)
In contrast, the research they've been doing at the Schaffer-Nishimura Labs showed that all mice that have Alzheimer's also develop stalls, and there's a certain pattern in all cases. This is one of the reasons why its so promising - if stalls occur in all cases, they may be linked to some fundamental processes in disease development, and by targeting them we can see major improvements. But still that needs to be done cautiously - e.g. initially in the lab they discovered a drug that reverses stalls, but it also severely impairs the immune system, which would obviously not be a feasible scenario for an Alzheimer's patient.
As each drug trial is subject to lots of regulations and is a long process, I guess even though it would be possible to set up parallel trials in principle, it doesn't really make sense. One team of researchers would usually focus on one type of a disease (if they take on too much, they won't do any of it fast enough!); and of course each disease needs lots of research before a drug trial can even be considered (can't shoot in the dark!). So until researchers can understand the role of stalls in vascular dementia, for example, or the molecular mechanisms involved, they can't really come close to a drug trial involving a drug that's targeting stalls.
Great question! Yes, and it seems there is already a drug that is in the process of being FDA approved for another disease, which could also help reduce stalls in Alzheimer's. In that case, I think what you describe would be possible - it would be up to the doctor to evaluate the potential benefits vs. risk factors, for example (as there would be no studies evaluating the effect of that drug in Alzheimer's patients yet), but it could be prescribed in principle. In any case, I'm pretty sure that for full adoption of the treatment full drug trials would have to take place. But it would be easier in any case, if the drug is already approved & out there!
Hope that answers it and apologies again for not doing it sooner - I've had a tab open with this question for weeks! But I tend to self-doubt a bit when it comes to biomedical questions, as even though I have the background, I am not involved directly in that aspect of research in this project ! but hopefully I didn't confuse things too much