What do you consider to be the most important drills for a player to become a better hitter and why? Some examples might be batting cages; live pitching; soft toss; hitting off the "tee"; dry swings; Barry Bond's drill; face the fire drill; etc.
1. Tee
2. Visual focus drills for the eyes
3. Live pitching (without any comments from moms/dads/coaches ... comments like "you shouldn't have swung at that pitch" "you should have swung at that" just destroy everything that they learned and could have made adjustments for if they were just left alone.)
A subset of your question, my three go-to * tee * drills these days:
After many years doing a variety of tee drills that I no longer have our kids focus on (top hand, bottom hand, staggered feet, on knees, etc) I find these three tee drills can really help tune in/fix an experienced hitter:
1) loading the back hip from fully closed, 3/4 and regular stance in a sequence, bat on shoulder or deltoid -- great for feeling load and hip turn/bat whip
2) walk up drills (which I prefer to face the fire, but really the same thing) -- great for weight transfer
3) moving tee high (especially) and inside/outside -- high is great for bat/hand/elbow path fixes and inside outside for reinforcing a variety of things.
3b) honorable mention: hand-over drill, if extension is an issue
That said, for younger hitters, the tee is also obviously great for *building* a swing from the ground up using more basic drills such as matrix, stop on contact, etc. And for any hitter a mix of tee, side, live etc. work is key.
But I've found this summer that the three (plus one) tee drills above if done well and consistently can generate real results against live, in game pitching.
What we call the walkup drill the girls call Happy Gillmore. Basically start one step out of the box. They take one step in and hit ( if you watched the movie Happy Gillmore, how he hit his tee shot ). Much like a pitchers walk through, gets the momentum moving forward and works on balanced weight shift.