I have an admittedly ambitious generalized theory of green speeds, which I see as exceedingly difficult to communicate because it relies on multiple variables and is course dependent.
To start, I'm assuming we all agree that consistency is paramount, and so when we are talking about green behavior, we assume it's consistent across an entire course. After that we have the inherent conflict between the strategic school and the penal school, and I'm firmly in the strategic school as I expect most of us are, so much of what follows is likely not particularly relevant to the penal school, in which greens should be generally straightforward to reward the player for reaching the green as directly as possible. I think for the penal school: faster -> flatter, and faster & flatter = better.
With that out of the way, the first point I want to make about higher green speeds is that, on the putting surface, contours should be effectively relative to green speeds insofar as making the ball move. Generally speaking the coefficient of kinetic friction can be compensated for simply by reducing the amount of potential energy, and we this by reducing the height of the contours. There is a major difference here in the amount of static friction, which I do not think is proportional, so getting the ball to stop will be more difficult on faster greens, which means it's wildly more important to be below the hole on faster greens, even if the contours were proportional to create the same types of putts. This means for an
existing green, increasing the green speed should increase the difficulty, which is why I think it's so tempting for folks to chase faster speeds.
Most importantly though, with faster greens, there is a maximum height of contours possible before the green becomes unpinnable, and as the size of the contours increase, the pinnable area shrinks.
That's the naive view of green speed... where we look at greens from the perspective of already being on the green. Where it gets interesting is when we start to consider the effect of contouring on approach shots:
Generally speaking, higher shots have more distance control than lower shots. This seems to be a dominant strategy in golf (we hit a wedge into greens instead of a running shot, because we have more control over where it ends up, thus a smaller dispersion pattern). Also generally speaking, the only counter to high-shot dominance is
high winds, and this is one of the reason why I think links golf has remained so relevant and consistent over the years, even while many parkland courses have inflated in length.
However,
if we wanted to, we could actually use contouring to favor running shots over high shots. This can be achieved because the velocity vector of a ball contacting the green from above is
extremely different from one contacting the green from along the ground. Here, the same large contour that will eject a high shot off the green
could funnel a low shot onto it, and the opposite could be true depending on the shaping. This effect is magnified with the height of the contouring. The larger the contours, the more the architect can incentivize and disincentivize different launch angles from the player. I see this as a
massive benefit to course design, as it creates another variable with which to test the player.
Here, on strategic courses, especially ones where high winds are not prevalent, since we do not have any
high shot specific hazards, if we want to increase the strategic benefits of different approach positions to different pins, we ought to run the greens as slow as is practicable, as long as we don't creating genuine problems with the static frictional forces being so high that putts stop being generally consistent. By doing this, we should be able to give the architect additional tools to create risk/reward payoffs to playing the same hole in different ways, where they can make a running shot more valuable to certain parts of the green, and a high shot more valuable to others.
The biggest issue with this view of green speeds is that it's really only relevant to potential courses, not existing courses with existing greens, so you can't really think of it by thinking of an existing green complex and adjusting the green speed for different outcomes, because you'd have to literally adjust the height of the contours fairly significantly to understand the value of slower green speeds.