Is applying to 20 graduate schools too much?
Just my opinion: Do you really need to apply to 20 schools? I think it is very hard to be focused when applying to many schools. You also have to spend lots of money, and more importantly, you have to find referees willing to write 20 recommendation letters! 

I have read many articles and most of them suggest 6-8 school: 3 reach schools, 2 match schools, and 2 safe schools and that seems reasonable.

20 seems to be too much and a waste of your time and money.