Just for fun, interest's sake and comparison, test the difference...
Grab a frame with stamped or pressed steel drops and, using one hand, try to squeeze them together. Now, do the same thing with a frame sporting forged drop-outs. My experience has been that the forged drops don't move nearly as much. True, there are other factors that impact this test but my money is on the forged drops, as opposed to the stamped steel ones. And...
Keep in mind that we are talking, mostly, about racing bicycles that are designed for competitive use. As an ex athlete (used to wrestle at the collegiate, national and international levels), I know that I would do everything I could to prepare for competition. That is the same situation that presents itself to the professional bicycle racer - he will pay attention to the details, seeking the best possible machine he can to increase his, or her, competitive edge. With that in mind...
He, or she, will opt for the stronger and precision made forged drop set, the lighter tube set, the better functioning components and the like. He, or she, will not try to compete on a department store offered entry level gas pipe road bicycle. It would be foolish for him, or her, to do so assuming that her or she wished to be competitive.
That is all just my opinion, of course, but if you take a look - virtually all high end road bikes, mountain bikes, hybrids and just about anything else high end will sport the forged drops (not sure how this applies to BMX since I have absolutely no interest in that style of bicycle).
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"98% of the bikes I buy are projects".