Can it be useful making resonator with lower Q for wider-band tuning VCO?

If you also want a higher noise VCO.

Lower Q means higher sideband noise.

De-Q'g VCO tank has nothing to do with tuning range. Just makes a lower Q with same tuning range.

If you want wider tuning range it is best to bandsplit tank with discrete parallel caps that are switched into tank. The switching in process will have some detrimental de-Q.

Most cellular I.C. and many synthesizer chips use this technique for very high freq (2-8 GHz) LC VCO on die that is bandsplit just for calibration to compensate for poor manf. tolerance (15-30%) of on chip VCO. The 2-8 GHz VCO is divided down to whatever freq (lower) needed.

The actual varactor or voltage variable capacitor for VCO tuning fed from phase detector is kept to a low tuning range to keep Kv low to improve loop gain performance.

If your Kv on VCO is too high then it becomes very difficult to clean up the phase detector output enough to prevent bad noise and jitter performance. Any misc. noise (digital/power supply/switching power supply noise) that gets on a VCO control line of a high Kv VCO just screws up general noise performance.