I'd say the answer to the OP is "it depends". If you're a younger guy and you want to really get better and want to put in the time, then yes, get the lessons. I'm 64 , a 12 hdcp and pretty happy with that. Would I like to get better? Sure, but not at the cost of hours at the range. If I can buy a club that will help me improve , why not? Guys change putters all the time, update their irons, etc. Why not just learn to hit your old clubs better? We all buy new clubs to help our game and swing faults in some way.
My problem is the opposite. I hit a draw and sometimes a pull draw that gets me in trouble. So I went out and got a fade biased driver with an open face (not adjustable) and now no matter how hard I go after it the pull just stays straight down the left side in a worst case scenario and usually fades back. Easy peasy. I have room in my bag to carry two drivers so might carry a fade and draw driver. All without having to change my swing. I usually lose at least 2-3 shots from pull hooking one out of bounds or at least into the trees where I have to punch out. If I eliminate that I just knocked 3 shots off my handicap without changing my swing at all.
One other thing to the OP, you say your instructor doesn't want you messing with draw drivers? Couldn't be that if they work he's out some revenue could it? Just asking.