I have, and will tell you the real reason. It has little to do with literacy or education. It is because (warning, this is going ironic) Indian people are incredibly disgusted about shit and want to not think about dealing with it.
I'm Indian myself. For example, we think toilet paper is a horrible idea. You just clean your shit with...paper...and just leave it like that? That would not fly, even in any of the villages you mention. They have to have water to clean their shit, usually supplied in a small bucket or vessel. https://en.wikipedia.org/wiki/Lota_(vessel)
Now think about temperatures. The current temperature at many places in India is more than a 100 degrees Fahrenheit. Your average restroom or shovel pit or whatever is going to smell incredibly bad and be full of flies and a horrible smell. That is why some people prefer the river, and don't use the toilets that are built for them (links elsewhere in this thread).
Solutions? It's a usability problem. Bidets for poop washing that can be filled up instead of using piped water, super hydrophobic coatings, really large pits (so you don't smell the waste) –- things like that are going to be the solution. Unfortunately, no one approaches it in that way, and prefers to go the route of "Let's teach these uneducated savages not to shit where they eat." This is very unfortunate and I hope it will change in the future.