I've read in various places that crystal oscillator ICs require very clean power (as opposed e.g. to your usual 3.3V rail from some switching regulator) and one way to achieve that was via LDOs. (Ref1)
However, the only thing that LDOs actually achieve is to stabilize the voltage against low frequency variations, perhaps out to several 10s or 100 of kHz. In contrast, XOs run at 10s of MHz typically, where most LDOs are completely inefficient at cleaning anything. Capacitors or LC filters are anyway used around XOs to provide sufficiently low supply impedance at the switching frequency. To be clear, yes LDO datasheet do claim high rejection at 10 MHz with suitable output caps, but this is not due to the active rejection, but because of the passive filter formed by the output cap. A passive LC filter likely achieves better rejection at 10 MHz than LDO + output cap.
The only reason in favor or powering XOs via LDOs would be, if their frequency depended appreciably on the supply voltage. However, this doesn't seem to be the case as shown e.g. in this datasheet from Abracon. Something like 100 mV low frequency ripple (which LDOs can clean well) would cause only something like 0.1 ppm frequency drift, if at all.
I am a bit puzzled by reference 1 above. It shows how low frequency variations of Vdd cause corresponding low frequency phase noise, but how? Wouldn't the oscillator frequency have to change to cause phase noise ? Or is that couple of ppb frequency drift enough to cause the excess phase noise ? 0.1 ppm of 10 MHz could only cause phase noise up to 1 Hz offset if I understand correctly (probably don't).
The application I have in mind is for a precision ADC (not RF). Therefore, close-in phase noise between 10 Hz and 100 kHz is especially relevant.
So what is the benefit of powering an XO via an LDO (plus capacitors around the XO) instead of a basic LC filter that lets all the low frequency ripple through to the XO ?