The dial controller sounds great, but I don't understand what it has to do with Space Invaders. Space Invaders didn't use a dial controller, and had it, it would have sucked. Is Space Invaders Extreme (2) designed for it, and if so, how is the game also good without it? Since I've got a DSi, the paddle controller isn't an option anyway.
The game doesn't suck without it but it definitely adds a new level of control. You're right, the original Space Invaders arcade machine didn't have dials, it used a left and a right button.
I didn't buy the controller for this game but this game and the original are two that support it, and are both games made by the manufacturer of the controller. The controller didn't come out in the US, and both Space Invader Extreme games are very playable without it. Arkanoid suffers tremendously though and that was primarily the game I bought the controller for.
I played the final level with the controller a bit ago and it's like a new game. I imagine the new more accurate controls come into play more on the harder levels.
edit: The first game I remember in the arcade with a dial was Tempest. Like I said I'd love to see a Tempest 2000 conversion that supported this controller, and even an Ikari Warriors would be sweet. Maybe some sort of tank game. I'd be surprised if we ever got another game that supported the controller though so if these two games and Arkanoid aren't enough I wouldn't recommend dropping the $25. Maybe homebrew/emulation can do something with it, I haven't looked into that scene recently though.