1W is a fairly massive amount of power though, a typical small DIY project will output a couple of mW. So unless you very explicitly start amplifying it after your oscillator there most likely will not be too much power radiating out unless you hook it up to another stage or a directed antenna (which gives you a passive way of boosting the radiated power by concentrating the output on a more narrow angle).
Yep, you're right. However, since Walkie-Talkies' power is around that level, I thought it'd be a good example to build upon.
Regardless of the power level, thinking about spectrum and trying not to create harmful interference is important IMHO. I live in a place where listening FM in stereo mode is impossible due to interference and radio transmissions around me. Even Wi-Fi cannot penetrate beyond next room.
We've looked how spectrum looked here with a listen-only SDR. It wasn't pretty. My friends' exact words were "Dude, that's not what I see at home. This is some serious traffic."