If they include proper integration capabilities then I don't see a huge issue with that.
But Capita are highly unlikely to make this sudden change. Why would they? They aren't losing customers at the moment, the money is coming in nice and steadily. They've got loads of third party partners integrating with their systems.
Reason not to use S3? Because its yet another tool for updating software where there doesn't need to be one. Use systems that exist already. But maybe that's just my '*nix' thinking coming out - use existing tools, string them together and do the job you want, rather than reinventing the wheel and increasing your development costs.
Capita keep saying that there are schools that don't have the capability to run such a setup? Its about time those schools modernise. Centralised network management has been around in schools for over a decade. If some schools still don't have that sort of setup, then they're a little behind the times.
You can't support every little odd, non-standard, setup. But you can support standards and ask people to follow them.
Adobe release their flash updates via a catalog for SCUP and it works well. I just deploy the original setups via SCCM (can be done other ways too), and then WSUS (or in our case SCCM) keeps it up to date with all the security patches released. They release them pretty darn regularly too.