Kohler seems to have the not-invented-here syndrom...they like to do everything themselves. This means that the only place you can go for parts is them, in most cases. Their parts book looks like a phone book, and because there are so many variations, few stock them, sometimes, even the factory, so you have to wait for them to build one. If you are lucky, maybe days downtime, but it could be weeks or longer.
Toto is the largest manufacturer of toilets in the WORLD...they make things in large quanties, and if they get it wrong, it is very costly. Personal experience is they do their engineering, pick a good design, then go with it - they rarely get it wrong. Plus, the things like fill valves, and flappers, they use parts that are generally available and common, so they are stocked locally.