Ok, this is actually what I would consider a 'next-level' intelligent thing to do, but more so for certain circumstances.
If you mainly livestream then this is a bad idea. It will leave your channel looking desolate and you need to show prospective followers that you make a lot of content. So if you don't make videos and you only livestream keep them public.
If you make videos but livestream from time to time then it is best to make your livestreams unlisted after a few hours or so.
The reason for this is because when you livestream YouTube treats it like a new video. So as soon as the livestream is over it is now the newest video on your channel and therefore it is the video the YouTube is going to start pushing for you. This is going to take impressions from whatever video you most recently published.
Because the appeal of a livestream is to be a part of the experience while it is live they tend to not get as many views as a regular video after they are no longer live, which is basically a waste of those impressions. So if you make videos and you prefer that YouTube feed impressions to your video instead of your finished livestream then you need to make the livestream unlisted or private.