Safe Harbor protects the platform, i.e. Twitch, from being liable for DMCA as long as they make a reasonable effort to enforce the DMCA and to remove repeat infringers, ie. bad actors. If Twitch loses its Safe Harbor protections, then Twitch itself becomes liable for secondary infringement.
Safe Harbor was designed to protect platforms and service providers from that liability of the users who produce content within or on their services.
What this means: Streamers are liable for the content they produce for as long as Twitch has Safe Harbor protections.