There are several aspects to why Strength and Conditioning (S/C) is important in BJJ.
First there is the general physical preparedness required for the sport. You have to be able to move your bodyweight (and often a portion of your opponent's bodyweight) effectively (strength) and efficiently over time (conditioning). I see many people coming into the sport who lack this base level of general physical preparedness. For these people basic S/C training is almost required along with their mat time/technique work to progress in BJJ. But fear not, this basic level of physical preparedness is something that "any average Joe" should be able to achieve with some time and effort.
Once this base level of physical preparedness is achieved, many people can advance quite well in BJJ concentrating on technique but strength (and size) and conditioning will almost always have benefits. Given equal skill, a bigger stronger competitor will win most of the time (not all of the time) and given equal skill a better conditioned competitor will be able to win more matches (especially in a tournament) than a less conditioned competitor.
Having a skill advantage allows you to compensate or even dominate against a strength/conditioning advantage. How much skill is needed to compensate against how much strength/conditioning is debateable but why not have both skill and strength/conditioning? (and yes there is a trade-off between carrying muscle mass, speed, and "gassing-out" - but that's a discussion for another post)
BJJ uses leverage as a "force multiplier", but there still must be some force applied. (Mathematically, this is expressed by:
M = Fd
- where F is the force, d is the distance between the force and the fulcrum, and M is the turning force known as the moment or torque.) The magnitude of torque depends on three quantities: First, the force applied; second, the length of the lever arm connecting the axis to the point of force application; and third, the angle between the two.
In BJJ terms this means I have to be able to manipulate both my body and my opponent's body into the proper positions to gain this mechanical advantage. I have to be able to set up the lever and fulcrum/angle properly (skill) in order to get the maximum output from my applied force (strength).
The stronger I am the more my lever and fulcrum/angle can be less than optimal and still be effective. Most of us know from experience that the perfect technique we just drilled becomes slightly (or significantly) less than perfect when we roll against a fully resisiting opponent. Add in the fatigue factor and we get sloppier still.
As for the argument "isn't rolling enough?" to develop my S/C (especially conditioning). It is a good foundation and should definitely be a large component of your S/C.
BUT - rolling by itself may not be optimal. If I have limited time and energy to be my best at any endeavor, I want to "optimize" my training program. I can get stronger/more explosive by specifically coordinating my resistance training; and get a bigger "gas tank" by specifically coordinating external cardio with my rolling than I can achieve just by rolling alone.
Finally, a strength and conditioning program outside of rolling can play a major role in injury prevention. As a precursor, it prepares my body for the stress of rolling. As a supplement to rolling it allows me to generate a greater volume of work without (if done properly) the resulting wear and tear on my body (bruises, sprains, strains, contusions, and other damage from rolling) that a high volume of rolling alone would accumulate.