Depends largely on the type of variation.

Front Squats are very different from Back Squats, and there are lots of really strong folks out there that work Front Squats to up their Back Squats or to help with Oly Lifting.

DB work is often done to help prevent imbalances, since you won't be able to overcompensate for one side with the other. Same thing goes for single leg variants of lower body lifts.

Finally there are a lot of variations on lifts that can be done to help progress the lift, though arguably one of the best ways to build a lift is to work that lift. However, Pause Squats or Bottom Position Squats might help people get out of the hole. Deficit deadlifts might help with sticking points on your pull.

Since you're mostly focused on physique, it might not be as important to build your big lifts, but doing so will increase muscle tension when you lift and will get you more bang for your buck with lifting sessions. Try it out and see how you do.

The problem with completely neglecting even branching out to try other things is then you get messed up and imbalanced scenarios where someone can squat 405 but struggles to front 135, and other things like that. I can't see that as being an ideal scenario for improving physique.

If nothing else, mixing it up and doing different variations can be helpful even to the average person just in that it helps prevent boredom. Personally, I get really bored with doing the same lifts workout after workout. Changing things up and doing them differently helps keep me more interested and therefore more motivated.

On a physical side, my personal approach is that it's good to work your muscles in different ways to help increase overall functional strength. While I don't have any medical or scientific evidence to back this up, I think it's pretty clear that your muscles adapt to doing the same motion over and over. I say this because in my experience, even though I lift 4-6 days a week, if I add in a new variation for a muscle group, I end up with sore/stiff-ness for a few days following. I take this as an indication that I've worked a new set of muscles or at least worked the muscles in a way they are not used to. I don't see how that could be anything but beneficial.

Generally speaking, yes. However, time/energy spent lifting is a limited resource. You reach the point of diminishing returns rather quickly doing curls from 85 different angles. This time could be better spent training the big lifts.

This is not to say that isolation work is useless, just that you have to find the proper balance.

This ^ i use the compound movment i move most weight with and then another varitation slightly lighter and one isolation for most body parts,

I was actually wondering if there was any benefit on the bb row to performing the move variation underhand or overhand--- or if it was simply preference.

I've always done it palms down.

I find underhand tends to use more bicep, and some folks find it easier to keep good form that way. I do overhand as well as I can use more weight and hit my back a bit better.

This is not to say that isolation work is useless, just that you have to find the proper balance.

I whole-heartedly agree with this statement, but want to add that variations at lifts aren't always strictly isolation exercises, and for those movements I'm not sure the same applies. I feel the same way about varying rep ranges for lifts. Such changes can be quite useful, and while not strictly necessary it's important to understand the benefits of incorporating those variations into a program.

I think for beginners focusing exclusively on the basic compound movements is a good thing, since those are the most important and the lifter will be working on form and such. There are also examples of really strong advanced guys who got that way basically on just a handful of movements like the big-3. In general though, I think good intermediate to advanced programs should have some variations of the big lifts to support building that lift, and some isolation work to support building the musculature needed to increase your strength ceiling.

It just depends on your goals and what you're trying to do.

For maximum training economy EVERY movement you do should have a purpose. I generally stick to the main lifts on most workouts but if you have a reason for doing a movement, then go for it.
I've done some deficit pulls to force me to keep my butt down at the start of my deadlifts, I've done board presses to get used to handling extra weight for the bench press, I do neutral grip pullups when my shoulders are bothering me.
Variations are great for addressing weaknesses or working around injuries, just know why you're doing them.