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That would be a different jam design, though a good idea for sure. A custom signup sheet could work, but requires a lot of guaranteed commitment of jammers. The % of joined to submissions is sometimes as low as 10-20%. Imagine 4/5 of assigned days being "no shows", it just wouldn't work.
They knew games would branch multiple times (perhaps a lot, perhaps so much that the last day is just two or three base games all branched out).
They knew games would die off. This part hurts a bit for projects that were actually good, so I feel like a "revival" opportunity or a "recovery" day might work for future jams to address this. Like a "Dead Pool" of strong projects that were not continued, that could be continued on any future day (with the downside of being down a day of development)
maybe you're right... though something that I thought might have been interesting is if the games worked on were ambiguous. That's part of the fun in the original pass the game challenge series--seeing what a average game can turn into within a matter of hours. This is what I tried with Budget Doom.