Typewriters.

They had bars that needed to physically move, and so staggering them helped them not collide and get jammed.

If you imagine a bar coming from the center of each key towards your screen, you can see how the staggering was helpful. For instance, M misses J and K above it, naturally, but it also slightly misses I and the 8 above that.

It’s a great solution for a nonexistent problem in keyboards.