(I did mention in my other post I can sort of see why handwriting is a movement more akin to other ways we manipulate the physical environment - but in fact I use the "swipe" style keyboard entry on my phone, which is surely not that dissimilar - using my finger to draw shapes. Touch typing is certainly very different and hard to correlate with other actions we need to perform in the real world, in some ways it's surprising we're able to become so competent at it, though obviously our ability to make finely tuned manipulations with our fingers is a huge part of our evolutionary success).
Well like I said above, I think the spatial details of where you’re writing and where the thing you’re writing on is located and the details of the spatial arrangement of your writing itself are all part of it.
Though I'd also wonder if it's a tad more than a hypothesis given what we already know about memory both scientifically and, perhaps, from practices people have developed over time to aid memory. I don't know all that nearly well enough to put together the case, but the "memory palace" technique, which is ancient and apparently "tried and true" seems like a striking demonstration of the the basic spatial idea. If there's truth to that, I'd say my suggestion could be reframed as a strategy for using handwriting to aid memory rather than a mere hypothesis.
Regarding the "slowing down" aspect, as others have mentioned too, I'd argue again that this could be couched directly in well established ideas and understandings ... chiefly, I'd imagine, the processes of repetition, practice and synthesis that are essentially common knowledge. The slowed down process of deciding what you're going to write and how probably forces you into a cognitive loop that goes beyond the mere recording of information toward repetition and synthesis. My experience with typing is that the urge to simply record verbatim is more natural to the medium.
(I did mention in my other post I can sort of see why handwriting is a movement more akin to other ways we manipulate the physical environment - but in fact I use the "swipe" style keyboard entry on my phone, which is surely not that dissimilar - using my finger to draw shapes. Touch typing is certainly very different and hard to correlate with other actions we need to perform in the real world, in some ways it's surprising we're able to become so competent at it, though obviously our ability to make finely tuned manipulations with our fingers is a huge part of our evolutionary success).