When designing experiments, when exactly is a control group necessary? Question:
An experiment is conducted to investigate the effects of different surfaces (placed at an incline) on the "rolling speed" of a golf ball. Is a control group necessary for this experiment?

The answer provided:

No. In the case of this ball experiment, there is not a clear control group as there is no "typical" condition. Theoretically, we could decide that the typical condition is when a golf ball rolls on synthetic lawn turf, but creating this control group is not particularly useful; not all experiments benefit from control groups.

Why exactly isn't a control group required for this investigation? Couldn't a "frictionless" board or a board placed at a $0^\circ$ incline serve as a control?
When designing experiments, when exactly is a control group necessary and when is it not?
 A: In an experiment, you are generally trying to associate some effect with a possible cause.  Some experiments are qualitative, and the question is “does this possible cause have anything at all to do with the effect?” Better experiments are quantitative, where the goal is to determine how much of the effect is associated with how much of the cause.
In general, the philosophy of scientific experiments is that you set up a measurement which can be repeated many times, where some of the measurements are “exactly the same,” so far as you can manage, and other measurements are exactly the same except for the cause you are examining.  Measurements where the setup was the same and the effect was different tell you about the limits of your reproducibility; measurements where the cause was different and the effect was different can be used to establish that the cause and effect are related to each other.
For some effects it’s possible to remove the cause completely from some measurements: for example, a vaccine trial where some participants are given a saline injection rather than an injection of material derived from the virus of interest. That’s what a “control group” is.  But you can also vary the amount of the cause, and see whether your effect gets bigger or smaller. For example, you might have a vaccine trial where one group gets a sham injection, one group gets some particular dose, and another group gets a double dose. Then you could ask both whether the vaccine has any effect at all (by comparing with the control group) and also whether a double dose offers better (or worse) protection than a single dose.
But for other types of experiments, it’s impossible to remove the effect completely. You ask about a zero-friction surface: there is no such thing. You can vary friction, because friction is proportional to normal force, $\left|\vec F_f\right| = \mu \left| \vec F_N \right|$, but that’s a nontrivial result.
Your question about a zero-degree incline is an interesting one, because it was one of the first applications of the modern scientific method: Galileo’s discovery* of inertia.  At the time Galileo began experimenting, the scientific consensus was that the “natural state” of a moving object was to return to rest.  Galileo performed a series of experiments with objects rolling down inclined planes, and invented a technique for quantitatively measuring the acceleration.† By measuring the acceleration at many different angles, Galileo was able to extrapolate to the zero-angle case and propose that an object on a hypothetical, ideal, frictionless, level track would travel at constant velocity for ever.

$\!$* It is tempting, from a modern perspective, to call the zero-angle result “obvious,” as a commenter does under your question. But it’s important to remember that Galileo had to prove that “obvious” result, and overturned two millennia of incorrect consensus by doing so.
† This was before clocks, so the invention was nontrivial. Galileo had his rolling objects strike a series of low-mass reeds, so that they went tik-tik-tik-tik-tik on their way down the ramp. He adjusted the positions of the reeds until all of the “tiks” were equally spaced in time, and then could carefully measure the distances between them. My PhD advisor liked to talk about this as the earliest example of a general feature in experimental physics: to measure some effect precisely, figure out a way to turn it into a frequency.
