This is wrong. It would be true if you received all the cash in a lump sum as soon as you're hired, and you used it to buy stock, but if your cash "vests" in the same way as equity typically does then you'd lose out on the opportunity for it to appreciate before vesting like shares can.

Seriously? You think students would revolt after being given an interesting problem to think about for 15 minutes?

I'm guessing you've never taught math to undergraduates. Unless they are math majors, for the most part they really don't like being given harder-than-average questions, let alone open problems.

"Without fair warning"

That's the important part of this - the instructor didn't give it as homework. And yes, I've seen students freak out on their instructor en-masse for far less than a mission impossible homework assignment.

Would you want someone working for you for another two weeks after you've fired them?

Depending on the reason for firing an employee, employers often have to give severance pay which usually amounts to two weeks or more worth of pay.