In my case, the interval is set to 0.5 which has a slight delay but enough for me to not mind. I usually have a mental idea of what mode I am in at all times.
> Can I somehow change the cursor system-wide?
Check the arch wiki article on Cursor themes[0]. Generally,, DEs have nice support for switching cursor themes after startup. In either case, you would need to modify `xkb_swapper.sh` to set a cursor theme whenever the mode is changed.