No, because most 120 cameras either:
1) have counters and film advance systems that only permit the number of shots that will fit on 120; or
2) have a little window at the back, which will nicely fog the 220 film which has no backing paper to protect it.
By the way, 120 and 220 spools have to be the same, because the feed spool on one roll (220 or 120) becomes the take-up spool for the next.
The leader and trailer papers wouldn't be as much a big deal if every roll was hand assembled. But if you need to buy those leaders and trailers at commercial quantities and use a machine in absolute darkness and have sufficient volume to actually sell the rolls at a decent price, with reasonable profit, then they do become a big deal.
For 120, where volumes are still reasonably high, the backing paper costs the film manufacturers more than it costs them to make the film itself.
With 220, where volumes are far, far lower, the cost of the leaders and trailers would most likely cost the film manufacturers much, much, more than the film itself.
Add in the additional costs for customized edge printing, separate packaging, separate merchandising - you get the idea.