The time would belong to the PIC. That would not be me.
And as a CFI, I get why you believe so strongly in your point of view, but you also know that one size does not fit all. With my work schedule--which is never a set schedule--I use my instructor whenever I can, as often as I can. That's if/when he is available and if the plane is available. Recently, most of my blocked times have coincided with bad weather (which at times, cleared up later in the day). You can see how all of those things can limit someone with a non-standard work week like mine.
In my opinion, and with MY situation, I believe I would benefit greatly by taking what I learn from each lesson and applying it as often as I can. And there are a 100 things I can apply to each of those personal flights that has little to do with actually physically flying the airplane. Navigation with maps/VOR, working on making radio calls, seeing/feeling how the plane reacts in different types of weather conditions, understanding parts/mechanics better. All things, in the end, I feel will make me a better pilot. Hard to do now with a schedule not super conducive to sharing a plane/instructor with many others.
I know its fun to play devils advocate and turn this into something it's not, but there's no reading between the lines here. I have been transparent about what I am looking for.