If you're buffing before a pull, SCH SS is just as good as PLD (or non-job) SS. So, if you are in 4-man content as an SCH, there's about a 50% chance that you'll have a second person in the run that can help you stoneskin. Suddenly, instead of one skill with a ~5 second cast time, two people have to cast two spells with ~2.5 second cast times each. SS2 wouldn't speed anything up in that scenario, though it does make it easier. If you had a WHM and a PLD, you still need to wait the ~10 seconds for the WHM to cast all four stoneskins before SS2 came along, slowing everyone down.
If you're doing 8-man content and do not have a WHM, that means you have 2 SCHs. Chances are, you also have 1-2 PLDs. The argument is the same as the above - it isn't really all that much faster to have a single person cast SS2 than to have 3-4 people cast 2-3 SSs each. Back before SS2, having just the WHM cast SS on everyone took a very long time, and since WHM's SS is better than others, you all want the WHM to cast it and not the PLDs or SCHs. So, everyone would have to wait for 8 spells to cast instead of 3. (assuming an average party of WHM, SCH, PLD, WAR).
So, yeah - WHMs needed SS2 more than SCHs did, just because by definition, if you're having the SCH cast SS, chances are high that more other people can also cast it than if you're having the WHM do it. Split work is less work.
Also, for those who are complaining about SS2 due to the number of skills comparison, if you check some wikis like Gamerescape, they show SCH as having 13 Job skills, where WHM only has 5 (every other class also gets 5, except Ninja which gets 6 or 15 depending on how you count). Sure, you could argue that Embrace (selene), Embrace (eos), Fey Light, Fey Illumination, Fey Covenant, Fey Glow, Whispering Dawn, and Silent Dusk shouldn't count as job skills, but they are skills you get by having the SCH job. As far as class skills, ACNs get Sic, Place, Heel, Obey, Steady, Stay, Guard, and Away. That's 7 skills over CNJ, even factoring in SS2. Sure, you can say that all 16 of these skills are really just parts of Summon and Summon II, but how can you argue that they are extensions of Summon/Summon II, but SSII isn't an extension of SS?