Sure. But there are things that you teach and things that you train.
I hope people are taught that go-arounds are possible, even after the third bounce, but I'd rather not see them trained in bouncing three times and then going around. Except in a simulator perhaps.
And as far as going around with a broken nosewheel is concerned: I've seen it done. A microlight of some sort was visiting our (controlled) field while we were running one of our charity days (flying with sick kids). He bounced on landing, broke his noseleg and went around. He then had the decency to hang around in the hold (with a dangling noseleg) while we could get all our charity flights back on the ground and while a few commercials could take off. Only then did he land and block our runway for some two hours. No injuries, except to his pride.
