The only early problem was temperature, but that was quickly resolved
Not sure I'd call 1,500-2,500 years (depending on region) "quickly resolved"
Iron was easier to produce and cheaper than bronze
Absolutely not in the 14th century, on average/most places. As hinted at above, the heating continued to be an issue well into the middle ages. they could heat iron hot enough to work, but not to melt it with any sort of efficiency or scale (in Europe at least). You had to very painstakingly heat iron to a spongey state, hammer the impurities out manually, reheat, hammer, reheat, hammer, reheat hammer, exhaustively. Which is definitely more expensive.
Bronze you could just melt, skim stuff off, and cast to get to the same point as above.
Only with blast furnaces and puddling furnaces and powered finery forges and things did it start to compete in easiness. Blast furnaces only just starting to become known/popular on the very late end of DF's time period, and the other things much later.
yet there was no way to find a good source of tin for bronze.
Totally depends where you are. Britain had/has tons of tin. However, if you didn't have tin nearby, then iron wares might indeed be cheaper than bronze ones. But in DF times in Europe (which seems to be the culture based on in game items and the fantasy stories it is obviously based on), this would be due to the higher cost of raw materials overwhelming the lower cost of labor to equal an overall cheaper product.
(Edit: Actually, due to bronze being superior for most things, I guess it would also have a higher demand, which might make it more expensive even in places with tin, separate from the raw material + labor considerations. But that's getting way too complicated for a discussion about RAWs to change, especially in a game with no real economy...)