I was a TA for a few professors while in university and I'd assume that most of them would opt for the 'free' version of a TA rather than having to pay for services on such a limited salary (but I could be way off on that, just my first reaction to the idea of seeking them out as clients.)
Also, since a TA is involved in the material being taught and the main focus of a teacher's work is interaction with students and the subject matter it might be hard to really participate fully in that process as a virtual service provider.
I do work with a choreographer/dance instructor in NYC - but she's more an entrepreneur than what you have in mind here I think...
I used to be a Teacher and had to pay for my own supplies, so hiring help wasn't in the budget.
LOVE Tess' idea of the dance instructor! That just brings up a whole new niche I'd never thought of for VA's. People who teach private lessons of any kind, dance studio owners, music studio owners etc...
Most of them can't hire a temp. or a permanent employee, so to be able to offload a little to a VA might be a great solution! Especially in urban areas like NYC. I was an actress in NYC and you should've seen the apartment I took my voice lessons in. I don't even know HOW my Teacher ran a business out of it AND lived there, but she did. Her husband helped out a little with her business stuff, but she did most of it herself. She could've so used a VA. Just a few hours a month would've helped!
Great idea Tess! So, who's gonna corner THAT market?! Or is someone already working with this niche.