My experience with the Honda CVT in the HX has been that between 100K to 150K the starter clutch in the CVT will degrade and need replacement. I've heard quotes of nearly $4K to rebuild the CVT...most people either sell the HX or swap out for the HX 5MT at a fraction of the cost.
New technologies and theory implementations are making for longer lasting and more reliable CVTs though.
As far as the theory of a CVT being more efficient than an auto trans; the CVT is supposed to be able to hold the engine at the FE sweet spot once it is up to operating temps and all conditions call for FE. Obviously, if you floor a CVT equipped vehicle, it won't get the same FE as lighter throttle.
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