Not sure what you mean by quick improvement versus long-term improvement in scoring. Both are improvements, and neither should be ignored at the expense of the other, IMO. I agree that the higher handicapper should first develop their ball-striking so that those ugly, wasted strokes disappear. But they shouldn't totally ignore the short game and putting because, no matter how much they improve their long game, they will still need to get it up and down to save strokes and to sink those pesky putts.
You should. I've shared my research and opinions on this several times. ;-)
Quick improvement is 1, 2, maybe 3 strokes a round. That'll be about the limit for most handicaps (and < 1 for lower handicaps), though - long-term and larger drops in handicap are from the long game.
And I'm not talking about 36 handicappers.