Questions about resonator S11 coefficient on a Smith chart

Let's say we have high Q resonator used in reflection configuration. What concerns me is that huge dip in S11 absolute value at resonant frequency is near center point on a Smith chart. I may be wrong, but isn't it then impossible to use resonator at exact resonance frequency? I mean that we must choose a little higher or a little lower frequency, so S11 moves away from 50 Ohm point, so S11 vector will have some length, and then phase of that vector will be seen more clearly?

Which shape of resonator 's S11 curve is more optimal? For example cavity resonator 's s11 looks like circle on a Smith chart. Depending on coupling between resonator and transmission line, radius of this circle changes. There are information on how to optimize phase noise, but how about reliability? Isn't it better to choose coupling which give bigger radius, so bigger area of Smith chart is covered with S11 curve near resonance frequency? And then it be easier to find intersection between resonators S11 and oscillator required Gload curves? If radius is too small, then curves may not intersect or be too far away, so oscillator fail to work.