Of course you can. Every modern BitTorrent client allows you to download file pieces by their order. IIRC it has been a solved problem for at least 8 years.
That is just not true, ever since PopcornTime has shown us that getting pieces in order is a viable strategy, especially at relatively large scale (for the BitTorrent network). There hasn't been any significant shortage of availability linked specifically to that way of downloading.
You're the seeder. Initially you're the only one with all 100. And everybody's gonna download things sequentially.
Imagine 300 peers grab block 1 from you. Gonna be pretty slow, each peer gets 1/300th of your bandwidth.
Imagine those 300 peers finish block 1 and move onto block 2. Same bandwidth crunch. Although new peers can at least get block 1 from that initial cohort of 300 peers. But nobody can blocks 2 through 100 from anybody but you. Not ideal.
Now repeat the process for 3 through 100. You're gonna be the bottleneck for a loooooooong time for those remaining pieces.
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...now imagine we do it differently. Those 300 peers each grab a random block. This part's just as slow.
But once they have their initial randomly-chosen blocks, our bandwidth explodes. Each of those 100 blocks is now available from ~4 sources (you, and roughly 3 others). And you could even log off at this point, since there is a complete (distributed) copy of your file out there.
As more blocks are exchanged, the effective aggregate bandwidth rapidly increases even farther.
You are assuming all the peers start at the same time. It would be more fair to assume that the peers start regularly. In this case, the order does not cause issue.
But then you are assuming that people will seed for an considerable time (more that a few minutes) after watching the stream. If as many people do they do not seed then the last block will forever only have one seeder. (which would at least be the case for the last scene of the last episode of the last season, a point where you might not like buffering)
Bittorrent tries to maximize the benefit of its P2P nature by not sending the same blocks to more than one peer.
i.e. I'll send block 1 to one peer, block 2 to another peer. Then I can send blocks 3 and 4 to them (respectively), while they each send each other blocks 1 and 2.
If the protocol does not require it to be downloaded in order (I don't know much about the protocol), then presumably you should also be allowed to disable that feature if you do not want to play back the file immediately.
If everybody did it, that would be a big problem.
More to the original poster's point, my post answer's the posters question of "why doesn't YouTube just offer file downloads like Bittorrent?"
There are many clear reasons why; my post gave one of the more prominent ones.