The vast majority of the most junior Capts and FOs are doing plenty of 2 - 5 day tours though, so its something in your bid that's putting you in fallback not a fundamental result of JSS.
By limiting JSS even in your lowest BG to 4 day trips in a month on a short haul fleet you are seriously harming JSSs ability to create a roster. Surely it would be better gradually relaxing that limit and not going into fallback and at least getting some of what you want?