Hardware sprites (and presumably interrupts) made the Amiga mouse pointer move fluidly and responsively even when the CPU was busy. No complex graphics pipelines or laggy LCD screens to add further latency back then either.
We even see it now, sometimes called "hardware cursor" in various games settings, althought pipeline is much longer.
Just that old small hardware had little to no memory protection and very tight integration so stuff like that could be done directly instead of going thru many layers of abstraction