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It doesn't seem logical that I lose the ability to listen to music that I purchased just because the intermediary that I purchased it through has gone.It is very logical, and this is the point that many of us, advocates of owning over renting, try to explain to people, unsuccessfully. You didn't purchase a license to content. You purchased a temporary license to listen to a piece of content on a particular service - a license that's valid only as long as the service wants it to, and definitely won't outlive the service itself. Basically: you're renting, not owning. It's all there in the terms you agreed to. Except, of course, services design the UX to make it seem like you're buying, and not borrowing.
(EDIT: this applies to most services people use for music, videos and other digital goods, even when they offer you to "purchase" copies instead of paying subscription fees - like Amazon here, or Steam games. That said, I see there is an option to download MP3s from Google Music, so perhaps the licensing terms there technically give you permanent license for the content itself. iTunes would be similar, IIRC.)
> Do not the rights holders keep track of who owns licenses to listen to what? Shouldn't they be tracking this information on the other side of their business
They do not, because they don't want to. It's against their interests. With the way things are, they get to charge you multiple times for the same piece of content.
Let's be happy that books predate modern IP laws, because otherwise bookshelves and libraries wouldn't be a thing now.
> Purchasing a license to stream a specific item via a specific service is, literally, buying nothing.
Exactly. That's the big "secret".