I find it interesting that everyone's default mode is somehow that a developer/studio should be able to dictate what people show from their game and whether or not they can make money from it. Even though I find the idea of making money off of Let's Plays a bit silly as well, I honestly think it should be none of your business as a developer.
This is all part of a bigger picture where I think the consumer of media needs to have more rights, not less. People already mostly don't own what they buy, can't do what they want with it, etc., and further limiting that is doing no one any favors, except the people in the business that don't even play games themselves.
If the developer can't keep people from sharing the content, they're going to have to recover their costs from the relatively few people who actually buy the game, which means stratospheric prices. The only people who would by are the streamers who can commercialize their copy of the game, and rich people who just want to play. The rest of us would be stuck.
This is all part of a bigger picture where I think the consumer of media needs to have more rights, not less. People already mostly don't own what they buy, can't do what they want with it, etc., and further limiting that is doing no one any favors, except the people in the business that don't even play games themselves.