There are plenty of studies that suggest that a higher number of sets is better for building muscle, but no study I have seen addresses why it's true, if it is true.
Progressive overload seems to be the main cause of muscle growth, but if this is true, then progressive overload can be achieved even with a single set, why does anyone need more, I could never see the benefit of a second set.
Is there any research that addresses why multiple sets work better?
Schoenfeld and colleagues give away the plot in the title of their paper, “Resistance Training Volume Enhances Muscle Hypertrophy but Not Strength in Trained Men”. They conclude:
Marked increases in strength and endurance can be attained by resistance-trained individuals with just three 13-min weekly sessions over an 8-wk period, and these gains are similar to that achieved with a substantially greater time commitment. Alternatively, muscle hypertrophy follows a dose–response relationship, with increasingly greater gains achieved with higher training volumes.
And the list of studies repeating similar findings is quite long. Volume drives hypertrophy. Multiple sets works better because multiple sets means you are doing more volume.
A 12RM on barbell squat is metabolically costly. Subsequent sets will require significant compromise in either load or rep count. However, for a similar fatigue cost, I can do six sets of eight at the same weight. Similarly tired when I’m done, but I’ve done 36 more reps. The research says the 6x8 is a more robust hypertrophy stimulus than that 12 rep max effort.
You're actually somewhat on the mark. A recently published meta-analysis led by researcher Brad Schoenfeld showed that a significant portion of hypertrophy is caused by the first set of any exercise. The amount of stimulus for hypertrophy goes down with each subsequent set.
So if you were really strapped for time, you could do one really hard all-out set three times a week and get 50% of the gains as someone who does six really hard sets three times a week.
Though, this doesn't answer your question. Why doesn't the first set generate 100% of the stimulus necessary to grow muscle? Why does 18+ sets generate more stimulus than only 1 set?
Spoiler alert, nobody seems to really know. We know that more sets equal more growth, but nobody seems really interested in why it's not achievable in one set.
The current leading theory about what stimulates muscle hypertrophy is that you need high mechanical tension with high motor recruitment. That is, there is a high force applied to the muscle causing it to stretch out, and almost all the muscle fibers are working against it to prevent that from happening.
Let's say you move a weight that you know you will fail at 10 reps. Every rep, you attempt to move it as fast as you can. This means that you are recruiting ever muscle fiber you physically can. In the first 5 reps, the force applied to each muscle fiber is relatively low because everything is working at full capacity. As fatigue sets in, the muscle fibers won't be able to produce as much force as they could, so the tension the weight puts on each muscle fiber increases. By rep 8, you'd be struggling to get the weight up because there's now so much tension, but there's still a lot of motor recruitment. By rep 10 the muscle fibers are able to produce just enough force to eek out one set, and by rep 11 they just can't produce the necessary force no matter how hard you try.
Now having said all that, why are multiple sets be better for hypertrophy? At this point, we can only guess but likely reasons are:
A) It's an imperfect system. Just because you tell a muscle cell to grow doesn't mean it will listen. So even if you manage to do a perfect set, doesn't mean that you'd get 100% stimulus from it.
B) It's extraordinarily difficult to get full stimulus. Producing 100% full force for every single rep on a set is actually extremely difficult. Especially in subsequent sets. It may feel like you do, but chances are you don't. It may in fact be impossible unless your adrenaline is very high, and your mind is in a fight-or-flight mode.
C) People typically don't train to failure. Training to failure is quite taxing and often discouraged. It is often better to leave some gains on the table for a second set than it is to risk injury going 100% on a single set.
It's also possible to fail a set because you simply just didn't try hard enough; so you didn't use full motor recruitment which means you didn't get full tension. So some people think they went hard on a set when in reality they kind of just slacked it.
D) Some other mechanisms that are currently not fully understood.
