I am not sure that it is a fad but I don't think its is the future. I have marked online using Turnitin and there are lots about this that I like BUT it is not very portable and lengthy documents seem to be harder to focus on online than they are offline. Online marking is also limited to certain formats - marking posters or presentations doesn't work. So I see some space for online assessment of assignments (2000 word max) but other formats are still much better as they are.
hard to know, we have been using it for a few years on campus and whilst it means students can actually read my comments, physically it is far harder on the body and eyes even with a mega screen. Hard copies are far more portable which gives more freedom for marking papers on the run so to speak. However with bulk classes that brings its own issues as well.
I agree with you Erik that smaller length assessments are more manageable as too, a combination of multiple choice questions which can be marked automatically with short answer rationales if more details are needed.
My person experience with MOOCs have been that several have used peer marking which has resulted in some interesting feedback and has meant the workload is being spread around. Consistency of quality remains an issues with this method though.