Up until the advent of the very latest technology, schedules have been the only way a teacher could ensure that they weren't overloading their students, to some degree at least (too many subjects to ultimately prevent it). But like any advancement in teaching, when a better more efficient method arrives, it is important that it is taken on, regardless of any inconvenience in transitioning over to it.
Bear in mind however, that unless a technological platform can inform a teacher how many tasks their students already have, then they are ineffective in eliminating the potential overload scenario, and thus must still rely on the use of a schedule. This is the case for the leading homework managers in the market (except The Homework Degrumbler), which only show teachers a central calendar that is pointless as students in high school rarely 'share' a class, coming from electives as well as streamed core classes. These types of technological solutions then really only serve to become notification and tracking tools, rather than teaching and learning tools.
The info-graphic below outlines some of the inefficiency that a schedule presents compared to a solution that can tell teachers how many tasks students already have before they decide to set more. The graphic is presented by The Homework Degrumbler , currently the only solution that can perform this function.