Teachers request 60 from a student because the teachers know that some parents will send their kids to school with no pencils. Pencil redistribution.
Also... there are probably other decent pencils... but Ticonderogas are nice and they don't mess up sharpeners. A lot of the cheaper pencils are bad to pencil sharpeners that the teacher probably had to pay for.
I just bought 2 cases of notebooks (24 in a case), and God only knows how many hundreds of pencils and pens. They're dirt cheap during the summer loss-leader sales at Walmart, Staples, Kmart, Target, etc. It set me back a whole $50-60, and from experience, I'll have enough to last the whole school year for whichever students forget a pen/pencil, and for any students who don't have a notebook or run out of paper in their notebook.
And, yeah, cheap pencils murder the pencil sharpener; the graphite tips keep breaking off and getting stuck, preventing following pencils from getting sharp. I have to smack my pencil sharpener against the desk at least once a day.