Hm, I think they understand what you're saying, but it seems you do not want to agree with what they are saying. In every instance you mentioned the record companies are getting paid by someone to have their music played, except for Twitch Streams. None of the money generated by the ads shown on a Twitch stream or a donation or a sub is going to the record company even if that stream is playing copyrighted music 24/7. Radio, YouTube, Spotify, whatever.... all pay a fee for the music they play. You cannot argue that that doesn't happen. Saying that a record should be grateful for a streamer that is playing music doesn't change that all other media pay those record companies for the right to use their music... except Twitch streamers. If record companies want to try and get some piece of that money from Twitch streams, they have every right to do so.
Saying record companies shouldn't go after Twitch streamers because its good exposure is silly, even if true. Other forms of broadcast media pay a fee for the same or far more exposure, so to should streamers / streaming platforms (that is how they think).