If you look at this image, you have a larger frame 4x5 which encompasses both a mountain and the river and a person on the mountain, we also have a smaller square which represents a 35mm image of just the person and maybe a little bit of the mountain in the corner of the frame.
The characteristic you describe is real. In fact it is said of medium format (paraphrased here) that there is a great headshot in every 1/2 length or head and shoulders portrait; that headshot (like the crop the 35mm sized box in your drawing shows) is simply cropped from the original composition. Similarly if we were using 4x5 we may be able to shoot a nice full length portrait and crop out that same great headshot.
Switching film formats behind a given lens at a given aperture, at given distance from the film simply changes the crop (the crop is the composition/the portion taken from the entire scene in front of the camera that ends up printed on the paper), the effect on the print is essentially the same as if we crop after the fact using an enlarger (or crop a scan) to print from 4x5 negative.
There is no change in the DOF when we crop within these constraints but the subject matter changes so completely, and the importance (finished/printed size) of each subject within the scene (mountain, sky, trees, people, faces) changes so markedly, that IMO the cropping you describe creates a completely new and different photo; a completely different work of art designed to suit a different audience or intent. Using your drawing as a base just visualize moving your 35mm box an inch and a half in any direction, at that point there isn't even any overlap in content from your original 35mm crop. (Your drawing is fine and fit for purpose BTW)
This is a fun and important theoretical concept to understand but it's application has significant limits, most notably is if we are trying to shoot to get to a print of a "given" composition.
When I go out to shoot a full length environmental portrait, that is what I want and what I plan for; cropping a headshot out later doesn't need to be considered when I plan that shot, it just happens to be there. I choose my tools, like most, first to suit the geometry required to get the planned composition; the angle of view from my chosen camera position defines the optimal focal length for a given composition, not DOF. Once I have the focal length figured out, only then can I choose the aperture to get the DOF I want.
Also, the aperture is limited by the physical size of the lenses that can be mounted on a camera and supported comfortably.
It would be really tough for example to get 150mm f/2 lens to mount on any 4x5 field camera. The physical aperture size (f=150 so f/2=150/2=75/1) would be 75mm, divide that by 25.4 to get inches and you have a lens roughly 3" inside diameter. Need a pretty big lens board to put that in, and the weight would be considerable, much bigger and heavier than the cameras I own could handle. You might need some really deep pockets to get one built too.