@siod yes, mostly because of power consumption. You can run an ATmega328P on a 3V battery, but then you need to use 8MHz instead of 16MHz according to the datasheet.
As I replied separately, you don't want to use an inaccurate clock for async protocols like UART that require precise timing.

a bit late but a word of warning for anyone embarking on this idea: the internal 8MHz clock is very inaccurate (%10 according to the datasheet), which likely will break asynchronous protocols like UART. As long as you are using only synchronous protocols like I2C you should be fine. More details can be found in this excellent thread on stackexchange https://electronics.stackexchange.com/a/32433/216828