The whole point of the tournament was to demonstrate one's skills in Blacksmithing. To do this in the most efficient way possible, the participants would have to work with the most basic and necessary tools. If external items are permitted to be used in the tournament, this would damage the whole point of the tournament. Take for instance the use of mystery flames like want was happening now.
Since mystery flames were much more powerful than regular flames, they were very good in the refinement of metals and for blacksmiths, the purer the metal as well as the degree of refinement, the higher the quality of the end product. In other words, mystery flames have a passive effect of increasing not only the success rate of a blacksmith but also boosting the quality of the product.