With streaming, the service provider is generally also controlling the clients, so they should be much better off when it comes to client behavior.
In case of bring-your-own-client, the incentives are exactly the same: Clients would likely default to good behavior as network health equals user experience, and exactly like BitTorrent there will be neither punishment nor need for it if some clients disobey.
This is not a "punishment", and what clients to differs greatly.
The original spec for the original client allocated a portion of its bandwidth to random peers instead of known-good/preferred peers, so if you had no chunks you were basically bandwidth and/or peer restricted.
If you take the arch linux ISO right now and put it into aria2c to be a new, unknown client with no data to offer, you'll find that while it takes a few seconds to join the network, fetch metadata and connect to peers, you'll quickly saturate your connection completely without ever uploading a single byte.
If you wanted, a streaming network could use direct access or low-hop access as seeding incentive - seed to get slightly lower content latency. When the streaming client is controlled by the content provider, seeding is easily forced and topology could be controlled centrally.
Yes that's the intended behavior of HLS - the content provider advertises which streams are available and at what bitrates, and the client picks which to use based on the current stream performance and its own capability.
The server can control the stream by advertising a customized manifest to individual clients, although it's a bit silly. HLS is designed to be extremely easy to load distribute and throw CDN/cache proxies in front, and it's a bad sad that content providers are this bad at load management. :/
Either way, the assumption here is that you would swap out the client doing HLS with a client designed to use a P2P protocol, including the seeding portion and network health management.
In case of bring-your-own-client, the incentives are exactly the same: Clients would likely default to good behavior as network health equals user experience, and exactly like BitTorrent there will be neither punishment nor need for it if some clients disobey.