Steel didn't really become cheap until the invention of the Bessemer process in 1855, by which time the Industrial Revolution was well established, "And Iron -- Cold Iron -- was master of it all!"
That’s why I said “eventually.”
The changes in steel production rates in the later 19th century are staggering, going from a few thousands of tons per year to millions of tons per year in a very short time.
Steel, however, had gotten a lot cheaper well prior to Bessemer. While it had not gotten cheap enough to be used extensively for structural purposes yet, it became a lot more reasonably priced for its traditional tool and armament uses.
The most interesting thing is that the quality of steel has not improved, at least for tool/weapns uses, in close on 2,000 years. The old Japanese and Indian swordsmiths produced quality that has never been bettered.
OTOH, it might take an expert Japanese swordsmith a year to make one or a few blades. Such a product could never be inexpensive.