Coin cells are common in marketing of microcontrollers and the like and as such is somewhat a mark of reference. There are also a good amount of devices (eg BLE beacon trackers) where AA or AAA would be too large. But if you can, use larger batteries :)

Coin cells aren't the best for this kind of system. When the current is a few tens of mA (CPU + transceiver), even for a short while, the coin cell battery internal resistance goes up, lowering the voltage over the terminals. This means that as the battery gets older, the risk of a brown-out reset of the SOC increases, even if there is still capacity to run a load with lower current requirements.

You could to some extent reduce this by using capacitors to reduce peak current over the battery, but caps have leakage current too, so the actual lifetime could be less still. Damned if you do...