You hit the nail on the head with your last line.
Most of the reason why I do not carry a wading stick is that I consider an additional burden and largely unnecessary. Accidents can and do happen, but I think they happen most to the inexperienced or might happen with or without a wading stick. There is also the condition where one can be overconfident with a wading staff and…you could find yourself in trouble quick. If you do not have the skill to cross without one, you should not cross. In my mind it should be an aid not a crutch.
If water is running so hard I feel I need a wading staff, I might consider crossing at a different location or finding a branch in the woods. Also, I might not cross at all.
My footing and balance is pretty good. My training is surfcasting in the ocean. We swim out to rocks in the surfline and sometimes when the surf is up we get pounded by waves. Sometimes the rocks are uneven and really difficult to stand on without getting knocked off. Even with skill…dumb crap can happen: follow this link… Medic! - #9 by dwalker
In that case my surfrod can act as a wading stick. It is like a 11’ pool cue. Yet, it did not help because, that is the nature of an accident. A wading staff is not a safety device. If you want one of those, wear a pfd.
When I fish for trout, I limit my wading. I fish from soft water or the edges. I do not believe in excessive wading especially in deep fast moving water. I feel if you are in the water, you are reducing your stealth, and unless the water you are fishing is fast moving you are probably transmitting your presence. If I do wade, the water is often a foot or two deep and not really a danger for me, even if it is cookin.
If I limit my wading, then I limit my need for a wading stick.
This is not to say they are not useful, nor does it mean there are not conditions that having one might be helpful. Tom Davis uses one and it seems the nature of his water requires a lot of wading around in fast water. I have fished plenty of fast water that I have navigated without a staff. Water that had no shoulder to fish from. I have never felt the need and most of the guys I fish with also do fine without them.
I think the take away is to be safe even with a wading staff. Dont cross water that you do not feel you could without a staff. Practice good footing techniques.