I would argue "efficiency" is the wrong word for what we discuss. Efficiency means optimising resource usage while achieving goals. If we need flexibility to achieve our goals consistently (and you usually do) then flexibility is part of efficiency (and effectiveness and efficacy) rather than opposed to it.

Phrased differently: if you define "efficiency" to mean "optimise for a single proxy metric and not what you're actually interested in" then yes, of course efficiency and effectiveness will be opposed other than sometimes by chance. But that's a dumb definition of efficiency!