If you kept power setting the same then you'd be right. But at the back end of the drag curve you have to increase power to maintain the same IAS. Couple this with the lift effects of the flaps and you get a shorter T/O run. Gets more complex when you want to consider angle of climb vs speed to altitude. Different aircraft have got different speed/flap setting depending on whether you want maximum rate of climb (ft/sec) or maximum angle of climb (avoid large building/hill ahead). All depends on playing off the vectors between forward speed vs vertical speed. In most circumstances going faster (up to a point) will get you higher, quicker (in terms of lapsed time) but will also use up more forward distance (hence meaning you might not clear an obstacle ahead).