Nor have I. I know some whitewater open boaters who eschew painters of any kind on their boats for fear of entanglement.
The Canadians and Brits seem to favor a fairly long painter stowed in a bag secured at the stems of their boats, long enough to use for lining the boat through a rapid.
My practice has always been to use a painter about the length of the boat itself or slightly longer, attached to a grab loop running through the hull itself. The painter is looped under a double shock cord that runs through the deck plate. On boats that do not have a deck plate large enough to secure a coiled painter on, I loop the painter under the cordage of my flotation bag cage between the inflated bags and the cordage in such a way that I can pull out as much length of painter as I might need.
I do know some very experienced whitewater open boaters who attach only a very short length of painter to the stems of their boats that hangs just above the surface of the water. This is just enough length that they can grab onto with both hands if they swim and need to self rescue the canoe or enough to use to tow a swimmer safely into an eddy.
A painter is very useful to tie the boat up to when needed but also for self rescue. I understand the concern regarding entanglement, but with the painter looped and secured under a tight double shock cord it will stay in place even it the boat gets tossed around in a big hole. I have used a painter many times for self rescue. If swimming with the boat I pull loose only enough painter to be able to easily hang onto the boat. Pushing a swamped canoe out of strong current into an eddy is not easy. It is often easier to pull the painter out, swim into the eddy, get your footing and then pull the boat in after you.
I would advise anyone using painters to avoid tying any knots or loops in the ends of their painters. They can and do get caught up in rock sieves which can hang the boat up in a place you can’t get to. Keep the grab loops short enough that you can’t get your whole hand through the loop. Likewise with any loop knots like bowlines or figure eights that you use to tie the painter to the grab loop.