> The alternative would be that each school develop their own platform for this
I worked at a university which did exactly this, in the UK.
It was a bespoke platform which integrated incredibly well with the rest of the systems the university used because it was designed from the ground-up to meet the institution's needs, there were regular user groups involving academics to understand what features needed to be built/worked on etc. At one point it was all OSS on GitHub too, in case other universities could've found it useful. It handled plagiarism detection (integrating with Turnitin), marking, exam grids, coursework submissions and feedback, seminar allocations, personalised timetables & mitigating circumstances.
The in-house dev team was vastly cheaper than anything SaaS would've cost, as well. It also maintained software for on-campus parcel deliveries, online exams, opinion surveys, a mobile app for students/staff, the SSO system, the course catalogue, car parking permits, a content management system and more.
