Did you notice that the peaking transfer curves in the figure are that of the partial (2nd order) filters. As already explained in post #6, Q is only defined for 2nd order filter. In so far, the Q measurement isn't applicable for the problem in post #1.
Also, as I mentioned in #5 and #7 it is not only necessary to measure individual Qs. You will have to see what discrepancy there is with the ideal Butterworth because although it is maximally flat as a whole, the individual biquads have peaks i.e. Q and droops that have to aligned with each other to get the final result.
I think this is quite specific to the application. There is usually a mask that sets the boundaries for the pass band, the stop band and the transition between the two. For example, Chebishev I type filers can have, say, 0.25dB of pass band ripple, or 0.5db or more. Which one you choose depends on your application. Similarly for Butterworth. Also, maybe a variation in the peak also varies the phase response and hence the overshoot of the step response. A model of your filter here can go ways because you can explore different scenarios faster.
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