Unfortunately, they still remain in some videos, and YouTube even seems to exacerbate the issue. In my opinion, the best solution to this problem would be for streamers not to include background music in the audio track of the stream in the first place. The second option is the new function for removing background music, which has appeared on YouTube, but it is still in beta and doesn't work very well.
In principle, the problem can be bypassed by recording videos directly during the stream, but there will still be nowhere to upload them, except perhaps to torrents; I have collected more than a terabyte of these videos in a couple of months...
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