Ok... to fix this analogy we're going to have to change some things. The game is not the instrument, the computer/console is the instrument. The game is the song.
Now, if someone was making loads of money covering other people's songs and not giving any money to the people who wrote the songs, don't you think that's a bit unfair?
Yes, but that's a much worse analogy. These people aren't taking games and releasing them as their own. If that's what they were doing, your analogy would fit. Watching a video of someone playing a game is not the same as playing it yourself, it just isn't.
Also, do you really think that Let's Plays are lowering the number of game sales? I'm pretty sure it's raising it. It's free advertising for the games, unless of course the game sucks, but in that case chances are that not many people want to either make or watch Let's Plays of it.
They are using someone else's material though. The LPer for the most part only takes the material and adds very little to it. Most LPs are just raw footage with terrible commentary added, and if the owners of the intellectual property want to complain OR prevent the LPer from profiting form it that's their prerogative. There are exceptions, though, where the footage acquired from the games is barely just half of what makes that particular LP special (Docfuture's Sonic 2 Special which has a shitload of editing and altering of things, it is a really interesting watch, Research Indicates's Jurassic Park Trespasser which is professionally edited and cut very well, Geop's Assassin's Creed 1 and 2 LPs which are half Ass Creed footage, half REALLY good history lesson). Strangely though, as far as I know they have not monetized those videos.
I for one have caused a couple of extra sales of some Atlus games with my captures, but that had to do more with showing off the base mechanics AND a basic guide than me being a good read or a good narrator, LPing does work as a showcase, but it should be more about the game and WAY LESS about the goddamn LPer.