The main advantage of a crystal oscillator over a tuned LC oscillator is:

Crystal oscillators utilize the piezoelectric effect of a quartz crystal, which acts mechanically and electrically like an extremely high-Q resonant circuit. This high Q (Quality factor) means the frequency of oscillation remains incredibly stable over time and across temperature variations. Standard inductor-capacitor (LC) oscillators are far more prone to frequency drift due to the thermal expansion of coils and minute changes in capacitance. While crystals are simple to use, it is their unmatched frequency stability that makes them advantageous in modern radio design. Note that crystal oscillators still produce harmonics and require filtering, so they are not free from harmonic emissions.