I rode for about 8 years with my hands flat, not bothering .
Then my life was transformed.
I had a lesson from another local RI and I was riding her horse, and she told me to turn my wrists and put my thumbs on top - she didnt want her horse ridden any other way, it wasnt kind to the horse.
Then she explained to me the reason for putting thumbs on top - the difference it makes to flexibility of the arms / reins and the sensitivity of the contact and feel between the hands of the rider and the mouth of the horse. And to the line of the rein between the horses mouth and the rider.
I cant remember the details - we need eml or someone to set them out, but I must have been totally convinced, because that one lesson made a profound impression on me and almost instantly I began to ride any horse with my thumbs on top on any horse - just to be kind to the horse.
I recently resumed hacking from a local RS - after a break due to illness and then sharing elsewhere - I noticed how my riding had changed since I was last there, in particular that my thumbs were now always on top. It isnt a duty, it is something I have done as a courtesy to the horses I ride, like when you shake hands with another person, there is something instinctive and well meaning about that contact too.
I cant really explain, but after a year or so of riding like that, it seems comfortable and natural - the only times I think about it particularlty is when I am asking for more collection or in canter. With your hands perpendicular with the thumbs on top, closing your fingers on the rein or opening them has a lovely effect on the movement.
Only I didnt learn or change my ways because it was the correct or proper way to ride - but out of politeness to the horse.