Friends might mention a band they enjoy, or you might hear a snippet on a video and look into it. Movie soundtracks occasionally have great music from well-established bands I've never heard of.
And you can go to live shows and check out local artists, buy their merch if they're any good.
Streaming is not the only way. Never has been, and never will be.
As far as your first question, is that a good thing, it's entirely subjective. But listening to a full album when you only "like" one song on it will expose you to new music, and might broaden your horizons or help you develop taste.
Or if you’re ripping your CDs and listening via apps you can just scrobble and get algo recommendations still while owning your music and without a monthly fee.