Wow! 2-3x higher strength is pretty overkill. 25-50% higher strength is more typical. Remember, higher strength concrete will require higher cement content. Even if they keep the w/c ratio the same your total free water content is increased which means more shrinkage.
Even in the cases you are mentioning that the higher strength concrete will push you into non-compliance with minimum As, doesn't ACI 318 have a provision that you need not be higher than 1.33 times the moment demand even if you don't satisfy minimum steel requirements. AASHTO does, so I thought ACI might share similar sentiments.
I agree that for a design concerning only vertical loads, there is no cause for alarm. However, there is certainly a cause for alarm if your analysis and detailing of the structure are relying on a certain level of ductile performance from your system under seismic loading. Whether you are running a force based or performance based analysis, the assumption is that plastic hinging will occur and that is why we specifically detail for these higher ductile system. Whether you are assuming your plasticity will occur in the column or the beam may never come to fruition if you are pouring 2-3x higher strength concrete. This significant increase in strength will change your moment-curvature results for a performance based analysis. When we run pushover analyses for existing concrete bridges we follow the recommendations of M.J.N. Priestly and take a 10% increase on steel yield strengths and 30% increase on concrete strengths. Material overstrength factors are something that should be considered as an underestimation of a concrete columns flexural strength could lead to grossly under designed shear and confinement steel detailing.
Short answer, yes, if you specifically designed and detailed for ductility based on expected lateral loads, I would be very concerned if the element intended to undergo non-linear hinging were poured with concrete strengths 2-3x higher than specified. If this issue is only concerning members that were considered for vertical loads only, then no, I would not be concerned.