Hm...might have to look at the wayback machine (I think Mr Happy's doing a video series of the Jobs through the expansions, though I'm not sure how far he's done due to the Ultimate race; he has done SMN, though, I know that). I very much remember in ShB players complaining that SCH's kit was gutted then, which means (on the whole), the playerbase DIDN'T feel SCH had been gutted in SB.
https://www.youtube.com/watch?v=B2mk...ZAoyf7&index=6
SMN still had Shadowflare, Bio and Miasma, Bane, etc. I remember playing SCH in SB and having Bane. I feel like it still had it in 5.0, though, since I remember spreading my DoTs in some of the early dungeons, but it may have been in SMN. They seem to have made Bio 1 -> Bio 2 in SB (in HW they were separate), but otherwise, SB still had the full kit other than that. They changed Shadowflare from an MP cost, 2.5 sec cast GCD Spell into a 0 MP, instant cast, oGCD Ability with a 60 sec CD, and the duration was halved while the potency was doubled (so you got the damage quicker). Miasma 2 was removed at the start of SB for both SMN and SCH, but was readded to SCH (since it didn't have a spmable AOE like SMN, WHM, and AST did), meaning SCH had Miasma 2 during the decline phase.
So it seems, at least on first blush, that the big removals were ShB, not SB. The removes at the start of SB seem to have been quickly reversed (for SCH), and the Job still had access to most of those things for the expansion. Again, first blush.
I'm not sure how solid a basis we can blame all this on "Well, SCH lost one DoT going from 4 to 3..." is as an explanation for the decline... It's probably one of those "maybe that was a contributing factor, but it wasn't at all the whole story or even necessarily a dominant cause".