I agree with many of your points. This is a great post. A couple things that stood out to me which you mentioned:

"Mage hand shouldn't be for pushing people, it should be for pulling levers, pushing buttons, and setting off tripwires and mines from a safe distance. The only potential combat purpose it should serve is "pull the lever to drop the chandelier" or some such."

Absolutely! I keep posting this where I can, but classes need greater demarcation. There should be many more things only a Wizard can do. Many more things that only a Rogue can do. So on and so forth. "Oh crap, here's some magical situation and we need a Wizard, my Warrior doesn't know crap about magic" or "I wish I had a thief to pick this lock!" situations really should happen. Another way to say this is there needs to be real class-related consequences.

Anyway, great suggestions all around!