I think my main issue with the offer is that it is MORE than just scheduling. It's managing a group of contractors, recruiting, etc.
I personally feel like someone with those qualifications is worth a lot more on the open market. I'm not looking for remote work right now, so I cannot say for sure, but I made more than that as a scheduler long ago, and so it feels low to me, especially in a world where remote jobs have become more of the norm.
These days you are also saving your employer a lot of money by not having them host you at an office, and you should be compensated for that. My current job shifted to be completely remote in the pandemic and may never return to a situation where I am required to be there in person. Anyone I work with who feels sick or or has somewhere else to be just works remote and attends meetings on Zoom, and it's not questioned. That said, you are also expected to still have someone else taking care of your children, and not have interruptions. It can happen occasionally, but office jobs turned work-from-home jobs are generally not a good fit for stay-at-home parents, as you are probably on the hook for more output than at an office, and subject to being called into a 'meeting' at any time.
Everyone at this MSC was very nice back when I worked with them. I just thought the work was too demanding and underpaid for what was required. If you tell me that this MSC is making the highest possible fee and barely staying profitable with these pay rates, then my opinion is that the business model is flawed. If they are making bank while underpaying shoppers and schedulers, then their business model simply sucks. Either way, something should change.
We often come down on shoppers here who take low fees and thusly bring our pay down. The same applies for the MSC employees. They perpetuate the problem by agreeing to to the poor pay rate. If the MSC could not get a scheduler for what they were offering, they would simple have to pay more. If they could not be profitable paying more, they would be forced to reevaluate their business plan.