Because other kids also grow too tall for their bikes, it seems to me it should be easy to find a good used one. I wouldn't be too worried about 'old steel ones', they are still road bikes made to go fast. Compared to the mountain bike you will reduce his disadvantage on the best bikes from minutes to seconds. That can easily be compensated by training on it and getting used to it. Competitive kids need good stuff to give them a fighting chance, not the best stuff that gives them an edge. He will just have to find an edge somewhere else.