The DMCA actually can protect streamers, just like any content creator, by ensuring that others do not use the content you created without your permission. But this also means streamers should not use content (such as music, graphics, characters, etc) that they do not own or have not obtained the proper licenses to use.
The DMCA, ultimately, is there to protect the service provider from the content created on their platforms. I.E. – The DMCA protects Twitch from the content that its users create on the platform so that they are not liable for that content.