Are You Being Too Specific?
The SAID principle implies that you adapt to the specific demands imposed, so to build a strong squat you'd perform a lot of heavy squats, or to improve your overhead press you'd do a lot of overhead press work. However in my opinion there comes a time for most people where being too specific and not having enough exercise variation can be detrimental to their strength gains. Not only can a wider variety of exercises make training more enjoyable, it can also be more beneficial than solely training the main lifts that you're aiming to build.
1) Greater Muscle Growth. We know that there's a strong relationship between muscle growth and volume, in that the more work you perform (up to a point) results in greater muscle growth. The crux of this point also applies to both higher volume and lower volume trainees. As strength trainers the 'main' exercises are pretty damn taxing, especially those that involve a large number of muscle groups such as squats, deadlifts, and floor to overhead press. This can pose a problem to getting in sufficient volumes to drive muscle growth, especially as an individual gets stronger and their training stress needs to ramp up due to previous adaptations (ie the training stress needs to be over and above what they've previously done to drive even greater adaptations).
What I'm getting at is that by solely focusing on the big compound lifts you're going to restrict volume as much due to systemic fatigue as muscular fatigue. This could easily compromise muscle growth which as we know is an important driver of strength gains because a muscle fiber with a larger diameter means greater levels of force production. The changes to the muscle moment arm also play a role in the transfer to strength gains as a larger muscle has more favourable leverages (if you have a tight bolt to loosen then a longer spanner is going to make it easier than a shorter spanner).
By utilising single joint movements (such as leg curls and triceps extensions) in conjunction with the main lifts you can still get enough work in to develop high levels of skill, but also increase your overall training volume in comparison to solely using the main lifts. For example you may well be completely wiped out after seven hard sets of squats, but could perform five sets of squats, three sets of leg press, and three sets of leg extensions which will likely result in greater muscle growth (without compromising skill enhancement of your squat) with similar levels of fatigue.
2) Regional Muscle Hypertrophy (RMH). Many people (including myself) dismissed the idea that you could attempt to target specific areas of the same muscle in regards to muscle growth but it seems that RMH is actually a thing and not just bro science. There isn't a great deal of research on this phenomenon to date but there's enough for Zabaleta-Korta and friends to have performed a systematic review of the literature and conclude that RMH occurs, but that evidence is lacking to securely state any relationship between a certain training mode and the hypertrophy of a given muscle region.
As far as it relates to training application a greater variety of exercises should tend to be more optimal for overall muscle growth as you'll increase growth at the distal (furthest away) end of the muscle as well as the middle and proximal end. Some research suggests that these regional differences are due to regional differences in muscle activation, meaning that some parts of the muscle have a greater strain on them thus should grow more. It's also been suggested that muscle fiber type could play a role - one part of the muscle may have a greater proportion of type 1 fibers that are less sensitive to hypertrophy, and another part may have a greater proportion of more hypertrophic type 2 fibers (this is also one of the reasons why muscle biopsies usually require three different sites in the same muscle because fiber types are not equally distributed within a muscle).
Eccentric training and using a full ROM are associated with greater proportional gains in distal muscle size and muscle fascicle lengthening whereas concentric only training and partial ROM are associated with proportionally greater increases in size of the middle of the muscle. When muscles increase in size due to lengthening it obviously doesn't change their point of insertion so they just bulge out a bit more in the middle (so the point from origin to insertion is further away).
The takeaway here is that performing a very limited amounted of exercises for each muscle group may short change your overall muscle growth which in turn could be detrimental to strength gains as discussed in the first point of this article.
3) You'll Be Stronger. I remember many years ago when I went to train with a very talented group of powerlifters and switched to their training methods. Previously I'd really focused on the main lifts and close variations but now I was doing a little more general assistance work such as cable rows, leg pressing, and isolated shoulder work...and I was weak. Well I was a lot weaker than I expected to be anyway, and if your goal as a strength athlete is to be strong rather than just being strong on a small handful of movements you'll need to include a variety of exercises in your routine.
Not only did I get much stronger all round but I grew more muscle which translated to improvements on the main lifts. As someone who got into training because I wanted to be strong it was also a bit of a reality check because even though I was benchpressing over four plates I was getting dusted on all sorts of assistance exercises by people who I would have considered weaker than myself. I didn't just shrug it off because I do think that machine based exercises and single joint exercises are pretty good tests of strength in their own right - when you drastically reduce the skill element you're in turn relying more on raw strength to shift the weight from (a) to (b).
In summary utilising a variety of exercises in your training program (whether that's all at the same time or in phased blocks of training) should set you up for greater muscle growth which in turn will transfer to bigger numbers on your main lifts. You'll also be strong on a variety of different exercises which is much cooler than just being good at a handful of exercises.