Usually when I see a 240v device, it is wired to its own double-pole circuit breaker, with each pole connected to a different 120v phase (to provide 240v total). If there is a 120v device in the same location, it is wired to a separate single-pole circuit breaker, which it often shares with other 120v devices.
If a neutral were wired along with the two phases in the 240v circuit described in my first paragraph, either phase could be used along with the neutral to power a 120v device. If there were no other 120v circuits nearby (and with enough capacity), this could potentially cost less than leaving the 240v circuit by itself and adding a separate breaker, hot, and neutral for the 120v device.
Why is the scenario described in my second paragraph uncommon in practice? Are there safety or electrical code concerns that I am unaware of?