Hi,
In answer to your first question this is absolutely fine and is how I use my Apple TV. If I'm just listening to music, I don't bother switching the TV on, I simply switch on the amplifier and use the Remote app on my iPhone to select and play music through the receiver.
As for the second question, it is simply a matter of choice. Many people do use e.g. a Mac Mini as a media centre connected to the TV screen. I prefer the Apple TV as it is a neater solution, has easy navigation using either the supplied remote or the Remote app on an iPhone/iPad/iPod touch. It is also instant on, so no messing about waiting for a Mac to start up, and no messing around with trying to use a keyboard/mouse in a living room environment. The interface on the Apple TV is also much more pleasant to use than the now very dated looking Front Row on a Mac.