Very astute, Birly.
There is much less "going on" with steel shafts in irons than with graphite shafts in a driver. With steel, you have a little bit of choice with weight and a small selection of bend profiles. Flex is predominantly the main fitting option for steel iron shafts. Because there is such little forward flexing through impact with an iron, and because the vast majority of golfers release the club early - the effect flex has with an iron is often reduced steeply downward. For the majority of golfers, weight is much more important than flex with steel iron shafts.
That being said, what the shaft (any shaft) does more than any other component is effect how the golfer swings the club. By altering just the shaft, I can alter how you swing the club and how the club feels. Ballistically, the head has the biggest influence on the shot. But how the shot feels, and how hard it is to perform primarily has to do with the shaft. The release point, tempo, path, etc. can all be altered by the shaft in the club. For good swings, the trick is to find a shaft that doesn't interfere with all those aspects.
Frequency matching is one of the most misused/misunderstood applications in fitting. If the goal is have all the clubs swing, feel, and play the same then MOI matching is your best means of getting there. Problem is it requires more work than most fitters are willing to do, and it is impossible for an OEM to offer MOI matching.