Re: Crosswind application(s)
Agree this is being overthought. The crosswind component on the ground will often be different - sometimes significantly so - to that on the approach. In the OP scenario I would probably turn onto a final of about 250, and if the standard approach speed was 70, probably use 80+, and no flap. (raises touchdown speed, improves control response, reduces drift angle).
The main difficulty I've had, as a PPL, with x/w, is when its gusty, as it usually is, and constant drift re-corrections have to be applied throughout the flare and touchdown. This is real life. In my job as an ATCO the only problem I have is if someone screws up and closes the runway. Hardly ever happens. OP, I think you're being far too academic about this. And I doubt very much your x/w limit is 20. You can land a cherokee/c172 etc with 25 (or more) x/w, but you have to seriously know what you're doing. This is advanced training, and not a training SOP at PPL stage.More likely your instructor wants to know you are capable of knowing when to say "No"