It is not the responsibility of the streamer to identify what infringes, but the party who files the DMCA claim
In your email you state
"For your stream archives (VODs and Clips), right now your only options, if you think they contain unauthorized music, is to either go through them one by one, or, for Clips, use the “delete all” tool we’ve provided."
This is utter ********.
When a streamer is alleged to have violated anything, that allegation should clearly refer to the video that violates, along with timestamps of the time ranges that violate.
Then, the infringing content can be taken down if it is deemed to violate DMCA.
You cannot expect that a streamer should pre-emptively go one by one through to "verify" themselves that all of their content does not infringe.
You cannot possibly be processing any DMCA claim that does not clearly reference the actual video and time ranges that violate.
Please clarify that to the streamer community that every DMCA takedown notice will clearly come with the target video in question and the time ranges.
If your guideline is that streamers should have the responsibility doubt themselves and their old recorded content beforehand to "save their *****" from a future ban. And they should pre-emptively delete content to avoid getting banned, you are harming the platform.
I have seen a number of streamers worrying about their content, since they cannot clearly know what infringes, and they do not clearly know if they can be held liable to a ban.
So please clarify how you are processing DMCA takedown notices, clarify the information that such violation allegations come with, and how the process relates to videos being taken down, or streamers being banned.