This answer will cover a lot of background information before getting to the point of the question. If one wishes to skip the background information, please proceed to below the divider.
Focus distance and depth of field scales on lenses were developed at a time when the cameras that used those lenses did not offer through the lens viewfinders. They give an approximation of what will and will not be considered acceptably sharp enough to be considered "in focus." Over the years, what we consider as "acceptable" has changed significantly.
Any estimation provided was better than nothing when one had no way to see through the lens to determine what was and what was not in focus. Many of the scales on such lenses were surprisingly accurate within certain constraints and provided great benefit to photographers who used them well. Since many photos created using such cameras were 'contact prints' that were the same size as the medium format negatives from which they were printed, the display size could be assumed to be the same as the size of the negative and thus depth of field calculations and indexing could also be made with a fair degree of certainty.
With the rise of 135 film (35mm) exposed horizontally in 36x24mm rectangles as a popular format, the assumption of contact prints was abandoned and what became known as the "standard" print size was an 8x10 inch print viewed from a distance of 10-12 inches by a person with 20/20 vision (Zeiss assumed 20/15 vision). The depth of field scales on most all lenses made for 35mm cameras assumed such a "standard" print size. If one where taking a photo they planned to print at, say 16x20 inches, one knew to halve the width of the DoF scales printed on the lens to account for the higher (double) enlargement ratio needed to produce a 16x20 print from the same negative size as the enlargement ratio used to produce an 8x10 print.
So as photography moved from large negative sizes and contact prints to smaller negatives and enlargers, the DoF scales on lenses became less relevant because the same scale could not be accurate for different print sizes made from negatives of the same size.
As photography and the tools used to do it progressed, the ability to see a very close approximation through the stopped down lens of what would be captured by the camera made DoF scales even less relevant.
With the explosion of digital photography and the multitude of different format sizes that often use some of the same lens mounts, as well as the widely varying ways in which digital images are viewed, today DoF scales are pretty much meaningless for most applications. The same image viewed on a 6" phone screen or a 10" tablet will have a significantly deeper DoF than when that image is viewed at 100% on a large monitor. When we view a 24MP image at 100% (zoomed in so that one image pixel equals one screen pixel) on a 23" HD (1920x1080) monitor, we're looking at part of a roughly 60x40" enlargement!
The factors that affect what looks "in focus" and what looks "not in focus" to our eyes are numerous:
- Entrance pupil ("effective aperture") size
- Focal length of the lens
- Film/sensor size
- Magnification ratio from the image projected onto the film/sensor to the image as viewed by an observer
- Display size of the image
- Viewing distance
- Visual acuity of the the viewer
The second through sixth factors above can all be summarized as the total magnification used. All of theses things combine to define how blurry something can be before our eyes see it as a blurry circle instead of a singular point.
Most prime lenses that used mechanical helicoids to move the focusing elements of the lenses had grooves in the helicoids that were straight lines cut into the surface of a cylinder. As the helicoid was rotated, the amount of change in focus distance per degree of rotation was not linear, but it was fairly constant along a well defined logarithmic scale determined by the angle of the groove with respect to the optical axis of the lens. Thus, as long as the distance scales printed on lenses were spaced using the same logarithmic scale as determined by the angle of the helicoid groove, things worked out closely enough to be useful.
Are there lenses where the distance markings on the focus ring (besides inaccuracies) would show a different behavior and lead to the DoF for a given aperture having different angular range at short focusing distance and at long focusing distance? For instance, on that 50mm lens, having only 5 degree from 7' 9.90" to 10' but 20 degrees from 26' to 100'.
I've never noticed any such prime lenses. But then I've never looked particularly critically at the distance/DoF scales on most prime lenses I've used. When I started doing photography TTL viewfinders and DoF preview buttons were already commonplace. Curves visible on the parts of the barrels of zoom lenses that were exposed as one zoomed the lens were fairly common.
I am asking this question because it seems to be a very strong
constraint on the design of the lens, particularly at a time where the
DoF scale has become unnecessary on most cameras and in most
situations as there are other (better?) options when needed (e.g.
visual inspection of the zoomed image on the back of the camera,
taking multiple shots, etc.). Without that constraint, would it be
easier to design cheaper or lighter focusing elements? Would it be
easier to design lenses with a shorter minimal focusing distance?
With the emergence of lenses that do not use helicoids to move the focusing elements of lenses, such as some 'voice coil', 'linear', 'electromagnetic', or 'nano USM' focusing motors, it is now possible to design smaller and lighter lenses. But it is not really due to being able to reduce the weight of the actual lens elements used to focus. Rather, it is due to the reduction in size and weight of the mechanisms used to move those lens elements.
As to minimum focus distance, the type of mechanism used to move the focusing elements has no bearing on that, assuming the maximum available amount of movement determined by the mechanism used is not the limiting factor. It's still all about the optical formula and the distances involved.
For any particular optical design, the focusing elements must have room to move further in a lens with a shorter MFD than in a lens with the same optical formula but with a longer MFD.¹ For lenses with focusing elements placed in the front of the lens, how far the barrel is allowed to extend is usually the limiting factor. For lenses with focusing elements placed somewhere inside the lens behind the front lens elements, the amount of movement the focusing elements can do before being constrained by the location of other lens elements in front of or behind the focusing group is often the limiting factor.
Where such focusing motors are giving lens designers more freedom is in the number of and possible locations of lens elements that move during focusing. From Roger Cicala's lensrentals.com blog entry linked above (italics added by me):
LEMs (linear electromagnetic motors) give lens designers some freedom they haven’t had before. The focusing elements can be put inside a zooming group. More than one element in the lens can move for focusing or compensation (this can be done to some degree with helicoid AF systems, too, but it could be easier and more flexible with LEM motors).
Such improvements allow compensating elements that can preserve the lens' peak optical performance over a wider range of focus distances. Whereas in the past lens designers might have had to choose between optimizing a lens for closest focus (macro lenses) or infinity focus (telephoto lenses), they can now maintain higher optical performance over a greater range of focus distances.
¹ Assuming both lenses are designed to be able to focus on infinity as well as their respective MFD. There are macro lenses that can only focus at the MFD with no longer focus distances possible.