I agree that an SSD would be a bit of a "waste" on an ATV1. However, I suspect that a good portion of the delays that you see within the ATV1 interface are the result of access latency on its HD. Thus, a PATA-based SSD might notably improve the UI responsiveness on the ATV1.
What I'm talking about are the types of delays you may see when the ATV1 is loading thumbnails from your media collection, or when you switch from playing media to go to the top-most menu (i.e. home). In the latter case, I often get brief dropouts in the audio playback of my music videos. An SSD might eliminate those types of problems but as others have noted it won't have much impact on plain-old video playback (once the video stream has begun).
The only real drawback to going to an SSD is the cost (duh!). I just can't see swapping out my 320GB HD upgrade for a much smaller SSD that would cost two to three times as much as a standard HD.