Stumbled upon this video recently…quicker, environment friendly-no plastic. See both videos.
I believe the machine is overkill, but even if we manage to have the paper ribbon + cups, the ribbon can be manually transplanted pretty fast.
On a separate note, I had something similar in mind for small seeded plants like onion and carrot. I was thinking of having the seeds glued to a newspaper ribbon so that they get spaced appropriately and then planting the ribbon in the soil.