There are oscillators that do have subharmonics. They are the Push-Push type of devices with two transistors. For example, each transistor is oscillating at 1 GHz, but because of the phasing of the Push-Push output structure, it looks like they are oscillating at 2 GHz. There would be a lot of 1 Ghz leakage though.
DDS's have harmonics as well as totally unrelated spurious tones, that can become huge as you approach an output frequency of around 1/2 the clock rate.
To get a pure sine wave out with the minimum of harmonic energy, you need to have a non-linear element in the oscillator circuit to reduce the active device gain to be "just enough" to sustain oscillation. Under this condition, the active device is not clipping, and produces low harmonics. Then you add a lowpass filter on the output for further clean up, and that is about as good as you are going to get.
But don't go nuts trying to eliminate all harmonics, because the very next thing you apply this signal to (amplifier, mixer, etc) will regenerate its own harmonics.