JF,
The bottom line is that a system can be analysed by applying any coordinate system you like, as long as the same system is applied rigourously throughout the entire analysis.
When looking at ressolving forces, far and away the easiest way of doing this is to use a coordinate system where the axes are at right angles (or mutually at right angles if you are doing a 3-d thing).
I'm guessing you are the JF who is a TP of some reknown. In which case I don't doubt that you will have been taught Aerodynamics at some depth, certainly by guys who know more than me. I wouldn't hazard a guess as to what coordinate system is used by Aerodynamics experts.
What I do know is that 99% of pilots are pretty vague about it, and the coordinate system I have described works pretty well for deriving most of the commonly accepted basic formulae of flight.
It is intuitive to visualise that drag is the force that slows you down. Therefore, where ever the aircraft is going is the best axis to define drag on - defining it back along the (tangent of the) flight path.
Having fixed the drag axis, the best thing to do (as mentioned above) is define the other axis at right angles.
If I'm not mistaken, I recognise your discusion point as the standard way of explaining induced drag.
I would say that it would be better to say that the total reaction has a bigger rearwards component than it used to have, so the drag has gone up, rather than talking about tilting lift.
May I point out a few possible weaknesses in defining lift as being at right angles to the chord line (and presumably drag along it?).
Imagine S+L flight. We typically have a small alpha in the cruise. Therefore our lift would not be defined 'up' but tilted a few degrees backwards.
(Assumption - no thrust vectoring)
Instead of L=W and T=D, you get:
(L Cos AOA) = W + (D Sin AOA)
and
T = (L Sin AOA) + (D Cos AOA)
Now, if you were to plug some numerical values (measured against those axes) into these equations you would get exactly the same results (i.e. that all the forces balance).
(like I said, use any coordinate system you like as long as you stick to it). Clearly though, the first way is a lot simpler.
Second observation. What do you do if you've got more than one aerofoil on the aircraft? Say a wing and a tailplane. Now you have two different mean chord lines, one for each aerofoil, usually bolted onto the fuslage at different riggers angles.
If you define lift as being at right angles to the chord you are opening a horendous can of worms because lift will defined in different directions on different bits of the aeroplane.
Much better to keep it simple and define lift at right angles to the flight path.
Hope that all makes sense. Its got late somehow and I wouldn't be surprised if I put a plus instead of a minus somewhere above.
Cheers.
CPB