People don't want a "gaming device" or a "music device", though. They want a single device that meets all their needs. Convergence is a compelling quality when you're carrying the device(s) around on your person. It's why mobile phones have single-handedly annihilated the practical wristwatch market, and why Apple launched the iPhone once the capabilities of mobile phones began to encroach on iPod's territory.
The DS may be the PSP's only real competitor, but the PSP certainly isn't the DS' only real competitor. In the long run, it or successor devices in the same vein won't even constitute the DS' primary competitor. Frankly, Sony's approach to the PSP as a "portable console", as much as it served to distinguish the PSP from the DS, is not going to work. If I'm looking to kill ten minutes then Bioshock isn't nearly as appealing as Bejeweled, and that is how most folks engage with portable gaming devices most of the time.
The iPod Touch/iPhone isn't there yet, for a variety of reasons, but in the long run it's going to be a very serious competitor to the DS. Nintendo knows it too, hence the DSi revision released recently adding a whole bunch of non-gaming related features to the device.
I understand what you're trying to say, but the fact is that no so-called convergence device does everything well. Most devices that aren't PC's have a singular focus, with the ability to perform multiple additional functions well.
The PSP and DS are primarily gaming devices, multimedia comes in second place for the PSP, followed by internet browsing. The ipod is first and foremost a music and movie player, with gaming being a tertiary capability.
My point is that if you're a gamer who wants to play quality mobile games first and foremost, you're going to get a PSP (or a DS) because you can't get games like Crisis Core, God of War, Gran Turismo etc on an iPod, it's just not a gaming device at its core, and until it gets a redesign that allows the use of buttons, it will never be.
Don't get me wrong, the ipod has some great games, and it's a wonderful platform for casual gamers, but Sony is first and foremost targeting the more hardcore gamer with the PSP. There is some overlap, particularly with the advent of DSi Ware and PSP Minis, but for the a person who is looking to play portable games as a priority, it's kind of a no-brainer.
I'd also like to add that there are a variety of gameplay options available on the PSP, if you want to kill 10 minutes, then games like SuperStardust HD, Buzz! or the upcoming Mini's are where you're going to want to look. A lot of the folks who buy PSP's also use the device in bed or on the plane or on long commutes, when they aren't looking for bite sized gaming.
It's also worth noting that despite the DS undisputed dominance in the marketplace, the PSP has shifted almost 60 million units worldwide, I think it's an unqualified success.