All of the components (hull, primer,powder,wad, and shot) in their individual packs will take up more space than flats. No argument there. BUT.... An 8# jug of powder and 3 boxes of primers take up very little space and is vastly more portable. Like I said, 3000 reloads from one 8# jug is the same as 12 flats. There are many great reasons for reloading. Currently, savings does not top of the list, but savings should not be the singular attraction to reloading.
A lot of trap and skeet people just buy winchester AA too.
Even so, I specifically pointed out that over unders are where you gain the most and compromise the least. Once you start having to feed from a magazine is where reloaders have an upper bound on their QC practices compared to commercial ammo.