It depends, but It turns out that your grip strength is probably more important than you’d imagine.
I heard a discussion between two guys from TV shows that strip participants of almost everything modern, forcing them to live primitively. Both participants were struck by how important strong hands were. Describing their time surviving as primitive humans might have, they said it was a constant grind. And also, that contrary to what you might think, surviving in primitive circumstances requires a lot of grabbing, holding, and twisting, but not much running or lifting heavy things.
That reminded me of a comment by Pavel Tsatsouline who has trained both Russian and US special forces. When he was asked what are the most important body parts to train, he said there were two, grip strength and abdominal strength.
Even in cultures that have specialization, sometimes grip strength is still important. In the Merriam-Webster dictionary under “dentist,” part of the definition said that “During the Middle Ages extractions were carried out by barbers and blacksmiths, or sometimes by specialist tooth-drawers, some of whom would spend hours pulling nails out of planks of wood as practice for extracting teeth with their fingers.” That’s grip strength.