I only wanted to bring up that the beginning of the sentence made it sound like a theoretical concept that might work, but no one has ever tried or seen in practice. The concerns are definitely valid.
Depends on the algorithm but you need not go 100% one way or the other. The basic rule can be 70% download next part and 30% download rare bits. The swarm is slightly less resilient, but seeders are still generally uploading the rare bits not the start of the file. This also tends to make a faster swarm as new downloads have something to trade.
You could have an algorithm change how pieces are requested based on availability (seed to peer ratio). If a torrent has high availability, then there is little harm in retrieving pieces sequentially.