That comment I made and the answer to it assumes that the goal is to primarily increase absolute strength with "hypertrophy" as a secondary goal. If your only goal is to increase muscle mass, then you probably wouldn't have things your considered main lifts, but I just wanted to clarify the intended audience.
The reason for not using a Main Lift for both increasing strength and hypertrophy at the same time, is because these can be conflicting goals. You cannot get your strongest on a particular lift while trying to do the kind of volume with it that causes significant and fast hypertrophy. Basically, trainees who do this compromise their strength and their mass gains. They are doing training that is not quite right for absolute strength, or for size. It is inefficient.
Sometimes people periodize mass and strength so that they start with a period of hypertrophy training and then move into strength. So, for instance, a period of higher reps followed by a period of lower reps. This is what linear periodization is or what is sometimes called Western Periodization. With that kind of training then you could use the same lift for both goals because you are not really pursuing both goals at the same time. This kind of training is not very efficient, though, imo.
The answer to the question will be found in all the various discussion in the GUS Hypertrophy versus Strength eBook.
The tired old claim that a "bigger muscle is a stronger muscle" is what fuels the perception that strength training should result in huge bodybuilderish muscles for all trainees and that therefore it makes sense to focus on the muscles to get strong. However, the key to gaining strength is to find ways to increase absolute force production. To increase force production, you have to exert maximum, or near maximum force against a load as often as possible. When you use the same lift for both the goal of increasing force production AND increasing muscle size through volume, you compromise both goals. From the book:
We can go ahead and assume that a bigger muscle is a stronger muscle [even though this is not precisely true]. However, if we consider the ratio of training volume/size increase to increases in absolute force production we realize that, again, training for mass in order to get stronger will never result in reaching our strength potential. There is a very simple way of explaining why. If we wish to increase absolute force we must be able to generate consistently high forces in our strength training. In practical training terms this means we must use high percentages of our 1RM. Not “fairly high” percentages. Not kinda high or sorta high. Very high.
Yet even those with PhD’s will make statements like this:
“To improve performance in a sporting event or an occupational task, strength training (e.g., weight training) is employed in the hope of increasing muscle mass and consequently strength.”
Training that has the sole goal for increasing muscle mass, does not increase force production in a direct way. You get bigger but you do not get stronger in a way that corresponds to that size. There is no linear relationship. So the kind of statement I quoted above, which is common, is asinine. It makes no sense whatsoever and this is NOT how people should train for strength. Strength is a goal in itself and you must focus on that goal to get strong.
Usually, for strength training, you would want to prioritize certain lifts and place them first in the lifting session and also first in the training week. For those lifts, higher intensities (bigger weights closer to max) should be used, and the volume will be lower..i.e. lower reps (although the number of sets may be kinda high sometimes). Then, secondary exercises or accessory exercises would be used to gather volume through the rest of the week. This will help increase hypertrophy.
That is not to say that you would NEVER use higher reps and higher volume, in general for the main lift. It is just that those parameters would be used because you needed to do that in order to keep increasing your 1RM, not because you were suddenly focused on mass.