I think that you have to be careful with the difference between Qu (unloaded) and Ql (loaded). Qu means the components are high quality, Ql should be as low as consistent with bandwidth. As Ql decreases, the RF losses decrease because the circulating RF current squared times the loss resistance decreases. It should really be 1 (or a transformer - no Q magnification of the input current).
Critical coupling is just a mathematical nicety, half power loss, double the bandwidth.
For a transmitter the working arrangement would be to have a Qu >100 and a Ql of 10, this would give about a 10% loss of power (as heat in the tuned circuit components). So for a 50 kW carrier power transmitter the losses in the circuit (mainly in the coil) would be 5 kW. If critical coupling was used the loss would be 25 kW, which is a lot of heat.
Frank
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Just remembered, your original question, does Q shift the centre frequency? The answer is yes but only very slightly, its a second order effect because the slope of the curve each side of resonance are assymetrical.
Years ago I was aligning IF strips with a nominal centre frequency of 250 KHZ, but all the circuits were peaked at 249 KHZ. The bandwidth as measure was symetrical about 250 KHZ.
Frank