The mouse pointer on Amiga was a sprite. So it flies above the bitmaps below, thence the 50fps frame rate.

If the Amiga's mouse-pointer sprite was removed and the pointer was rendered onto a bitmap, it would still be 50Hz. There is more than enough time to do that.

The flawless refresh rate comes from the fact the update is executed as part of a level 3 priority CPU interrupt triggered by the vblank refresh. Interrupt code reads the hardware register of a dedicated chip that has been measuring the mouse's potentiometers this whole time, to see how much they've moved. The mouse itself is a passive device.

It then sends a input event to Intuition, whose priority 20 input.device task (the highest priority task in any normal Amiga system) processes the event and updates the hardware sprite coordinates, but could equally write it onto the bitmap. It has the time to do that because everything else in the system waits for it.

Compared to a modern PC, which also uses a hardware cursor... the mouse is an active device and sends its own potentiometer readings as USB input events, which arrive to be processed by an independent USB subsystem in the kernel and is bundled with all the other USB traffic from devices attached on the same bus. A vblank interrupt couldn't get the mouse coordinates even if it wanted to.