> That rules out classes of problem which we want to teach
Does it? Could you give a contrived example of a high school problem that would be ruled out by a lack of a graphing calculator?
> Teaching students to graph
They should be able to plot any of the functions they'll be working with by hand, very quickly.
> statistical functions
If they are using statistics, they should be able to provide the relevant combinatorial coefficients as the answer (xCy, etc), without actually doing the computation.
Not to mention that scientific calculators all support basic stats functions.