The exam grading was handled this way at the school where I TAed intro chem-
There were 3 lecture sections of ~400 students each. All would get the same midterm and final, 4 to 5 versions each. After finals all the TA’s (30 or so) would sort the tests into version, A, B, C, D, etc. If there were 4 versions, we’d split in to 4 groups. Then usually, each TA would grade one free response question. So I would grade question 1, hand it off to the student grading question 2, and so on in a round robin. Then some TA’s would be totaling, double checking totals, and entering the grades in the system. 8 hours, many pizzas and Cokes later, they were all done. It sounds chaotic and industrial, but was generally pretty fair, because with the same student grading the same problem any partial credit was awarded consistently.
With 1200 students taking intro Chem every year, we had a full time employee (PhD) who did nothing but administer the program. She assigned the lecture section instructors (PhD’s), discussion sections(TA’s), labs (TA’s) made sure all the labs were organized and supplies were ordered, etc. She arranged subs if someone was sick. She also did an orientation/training for all TA’s and evaluated us. If you got poor reviews you would not be reappointed as a TA.
Unfortunately if you go to a school where 1000+ students are taking a particular intro class, it is goign to be organized in some such fashion. No school is going to break it in to 30 student classes with a PhD at each section.
But realize by going to a school like that you do gain some advantages over a small LAC. The large and diverse student body and campus offer other opportunities. And after the first year, you are pretty much through with those sorts of classes. And you may actually like some of your TA’s and form a relationship with them, you can even end up doing research in the labs they work in, or getting some fresher advice on grad school and such than you may get from profs.