Different strokes, I guess.
It's not like it
can't be done safely... but I was taught to not touch the flaps until after throttling up, retracting them in increments. If you do it that way, obviously it's important to start ASAP, and of course not forget to finally put them away (although it's not usually a great hazard to have too much flap down on takeoff and climbout). I really can't recall if the first flap change came before the nosewheel came up, or what... but it was definitely before taking off completely. Once on my own, I became more of a fan of full-stops, although I did go-arounds often enough.
I was put through T&Gs for the usual reason- to save time working on landings without a lot of taxiing- but also as aborts after touchdown (an unlikely necessity, but it could happen). I was encouraged to not dawdle on the runway in general... come to think of it, I don't think I ever did an actual "stop and go" during those training sessions (usually at KMMU or KCDW). The CFI who I did most of my T&Gs with liked to see me get going quickly, and that just became the normal way for me. I'd imagine the only real difference was that power came first, and the re-configuring happened on the roll and into the takeoff.
I agree, though, that this approach can tempt a student to rush, including advancing the throttle too quickly, or forgetting to turn off the carb heat, or resetting the trim. It makes sense to correlate the "go" part with a normal takeoff from a dead stop, and here's usually time- even if you
must take off again rather than roll out- to take a breath and think about what you need to do. Much as I was encouraged to take off again quickly, I'd also get an earful if I didn't do everything in sequence, and smoothly.
Speaking of carb heat and T&Gs, anybody else learn (in a push/pull throttle and carb heat setup) to push the carb heat knob in with their thumb while advancing the throttle?