Vessbot I am sure we're on the same page, perhaps viewing from slightly different angles, like two people sharing a read would.
That graphic is maybe the first figure in all of the Principles of Flight books out there, and cannot be wrong. You will find a thread where I argued against several more experienced people that it is with thrust how I control sink rate and chase the G/S on approach, even on a swept-wing jet.
However, it describes a static state with constant speed and AoA (which is why the latter is missing in the depiction). An attempt to use it to explain what happens in different places of the envelope as you change from one to another would not work. There are full volumes of aerodynamic theory beyond this drawing for this very reason, the drag polar being just the first next one.
E.g. the graphics cannot explain the difference between Vx and Vy, and we both know how vitally important those are especially if someone finds himself well slow of both.
I had a bit of resilience accepting
"Climb gradient is a function of excess thrust, nothing to do with lift." Took it the wrong way, not realising against the missing
"For a constant speed and stable AoA,,.. " was there, just silent. Culpa maxima.
The climb gradient after takeoff has massive amounts to do with how much lift you have to begin with, and that depends on the speed (squared) at the beginning of the second segment. Sure, drag does too.
During the take-off performance analysis we can select the V2 speed higher above the low limit, closer up towards best L/D speed, which then yields a steeper climb with the same amount of thrust applied, over-ruling the drag increase.
Once airborne in the equilibrium state, all that ammo is gone and the basic principles take over - it is the thrust (excess or lack of) which defines the changes of the climb rate if we were keeping the airspeed steady. No disputing there.
I'll wait for your closing public remarks and then we really should continue elsewhere to avoid floggin'.