While I believe the big barbell movements such as bench, squat, deadlift, OH press, and clean/snatch should be performed by everyone, barring some extenuating circumstances (and no, your back or knees hurting doesn’t mean you should skip deadlifts and squats; they probably hurt because of weakness in the posterior chain or around the knee joint), assistance exercise selection should be used to target any weaknesses.
Assistance exercises are an opportunity to bring up any lagging muscles that are either not working efficiently or not working at all in the big compound lifts. For example, if you struggle to engage your hips and glutes in squats and the majority of the stress is being transferred to the quads, there is no reason to use front squats (quad dominant movement) as an assistance exercise since they are already getting plenty of stress on their quads from the main movement. Instead, assistance movements should be chosen that target the weak points of the body.
This is opposite of what most folks do since it is much easier on the body and the ego to do what is easy and comes naturally, but, this type of training will at best leave them with a sub par physique and physical ability and at worst lead to injury or chronic pain due to muscle imbalance. With this in mind, the trainee having trouble activating the hip/glute complex should choose assistance exercises that target this area such as rope pull throughs, hip thrusts, glute bridges, GHR, etc.
With this, it is not enough to just pick exercises that are “supposed” to target the muscle groups you are seeking to activate, you must find the ones that work best for you and use/abuse the hell out of them until you can activate the musculature on any lift at any time.
Personally, I always had trouble activating my lats. Through experimentation with different exercises, I found that a variation of a high row machine allowed me to really “feel” the lats work. I started using this exercise on both of my upper body days with different rep/set/weights and made sure I really stretched at the top and squeezed at the bottom. After a period of this, I began to be able to activate my lats and feel them work in everything from bench press to RDL’s to OHP.
Once you isolate the lagging (or basically non existent) muscle group and learn to feel and use it on these assistance exercises, you will not only start to notice your big compound lifts moving much easier and fluid, you will start to notice nagging pains (lower back pain is very common with folks that sit all day and have inactive glute/hip complex) are either decreased or eliminated completely.
Pair this with the fact that you will look much better and have a balanced physique (think giant pec/bicep guy with tiny legs) and you have a few damn good reasons to start doing what you aren’t good at and stop massaging your ego with more stuff you are good at.