I do not know when steel banding first applied to lumber - but I have a related data point. I worked at Fisherman's Packing Corp. in Anacortes the summer of 1961 and I was in "the warehouse gang". One of our jobs was to prep pallets of canned salmon (already in boxes) for shipping out by box car. In that summer we transitioned from using steel banding (approx. 3/4" wide) to using what we called "super tape" - which was a 3M product and had long threads of nylon that were bonded to each other with some kind of flexible glue and had one side that was sticky. The sticky side kept the tape in the rolls and also kept it in place when applied to whatever it was holding. It was also about 3/4" wide and was used as a one-for-one replacement of the steel bands. The advantage of the tape was that it was a lot faster than having to use a special tool that cinched the steel bands and then applying a crimped 'keeper' to hold it. That tape was super strong - yet you could cut it with a sharp blade. It was so strong that I used just 2 strips of it to hold up the motor of my VW van that I was re-building.
I did see steel banding on wood loads -well- after that time frame. I think the load holding method that replaced steel bands was what is called "shed packs" (wrapped in plastic in a shed at the mill). - Jim in the PNW