If you want to forcibly learn to touch-type, learning Dvorak is a very potent solution. The reason why you don't touch-type on QWERTY is generally that, frankly, there isn't a very compelling reason to. QWERTY doesn't reward you for it. You keep your fingers on the home row, and you get, what, the J? The K? F? The semi-colon? WTF? Why would you touch type? I'm not actually sure failing to touch type with QWERTY is actually a problem. It may actually be the most rational reaction.

Or you can switch to a sensible keyboard layout, of which Dvorak is the easiest to get support for (though not the only, and, abstractly, not necessarily the best, but mostly good enough). Now you get AOEU under your left hand and HTNS under your right, and guess what, you don't have to try to keep your fingers on the home row, because they're just there anyhow. It's difficult to imagine what a "non-touch-typing Dvorak user" would even be, at least once you've really internalized it.

Given how painful learning to QWERTY touch type can be, it's probably easier just to switch to Dvorak, learn the layout, then just naturally learn touch typing in the next couple of months without "trying". The total effort might be lower, even if the switch isn't free.

(This is all assuming we just take as a given that touch typing is desirable. I'm not sure about that, but I also think we lack the data to be sure either way, especially when it comes to long term effects.)

Colemak is another good alternative to Qwerty layout. It's still not as popular as Dvorak (Colemak support was not present in OSX until Lion), but it seems to be beating both Qwerty and Dvorak layouts when it comes to speed and learning curve.