Interestingly enough, here's how this worked when I was an undergrad TA:
* The college's central office paid TAs for obligatory undergrad courses (so basically CS101 etc. up until sophomore year) * Advanced courses were funded by the individual chairs and institutes. And would you look at that, suddenly there was a whole less of code submissions auto-checked for plagiarism, and a whole more "talking to the TA to explain your reasoning and problems you encountered". This also served the double purpose that these TAs got to know the students, their likes and dislikes, and led to some easy recruiting for PhD candidates and such.
