Very few of the sites that I've seen tackle my key pain and time points. These are test correction, writing correction, and parent communication.
Why isn't there a cheap smartphone OMR program? Of course we all waiting for the Internet and fairies to take over testing, but until then I'd like to have a decent way to make, grade, and store data for paper quizzes. There's not really anything designed for teachers to buy out there.
Writing correction is a hard problem (since handwritten work is privileged in K-12) but perhaps not impossible with OCR advances. If I could unload some of the more mechanical aspects of this it'd be wonderful.
There is a cute and secretly useful free utility called Teacher's Report Assistant. This is the sort of thing that teachers will pay for, and for anyone who plays with things like chatbots its a natural extension. Huge masses of teachers all over Asia are churning out this sort of blather weekly. We could use help.
It's worth mentioning that there are masses of private schools in Asia and in the western world that have much more open policies about reimbursing for software and the like. It's not a bad path to bigger things.
Schools almost universally have overloaded and unreliable networks, so you have to have a reasonable offline path.