I have often wondered if this is the whole story on this.
Of course, in the days of BP, barrel makers had a good idea of the strengths of the steel they had to use and knowledge of what the barrel dimensions had to be to comfortably pass BP proof.
With the advent of cordite and other nitro powders, they learned that higher/faster pressure loads reqired stronger barrels but I am thinking the steels used in the early nitro guns were the same as the BP guns - especially in the transition period when BP and nitro guns were both being made. Nitro barrels did need to be built heavier in the breech end though.
IMO, to suggest that the steel itself was the weak link may not be the right answer - at least early on it was probably about the "beef" in the barrel.