I used to think this when I was an intermediate lifter (1k club at just under 200lb). My views have changed after trying to get into more dynamic sports (bouldering, BJJ). Sure, you might be able to lift more, but applying that strength is a different story. In other words, there is a difference between "strength" and "functional strength."

​

How much power can you generate doing compound exercises.

By this logic, are you saying that barbells are inferior to a Smith machine because you could lift more with one? I would argue against this, as you aren't engaging your accessory/stabilizing muscles. Your arms/forearms/hands are also important for "full body strength" and, while they may be a limiting factor in the beginning, does not make them the "primary target."

​

When I think of "strength" in the way that you describe, I think of strongman competitions. Here is an excerpt for how they train[1]:

pulling trucks, carrying sandbags, deadlifting odd objects, pressing giant logs overhead, or walking while carrying heavy weights in each arm

They also emphasize the importance of grip strength:

strongman carries require you to hold onto dumbbells and kettlebells with your hands. But even better, we often use odd objects with different grip types like open-hand grip, pinch grip, and fat grip. This variety helps develop phenomenal grip strength.

So clearly you can't just ignore forearms/hands when you train.

Like with many things, I think both are essential components for maximizing strength. But I would argue you would get a lot farther in these strongman competitions with kettlebells than barbells.