Right, maybe "You can cherish anything" would be more correct, because you can never be in the state of cherishing (or even noticing) literally everything. Anyway, the ability to experience aesthetically is arbitrary, right? Experiences are not intrinsecally aesthetic. It's you who bring an aesthetic dimension to the experience — rather, to the mental rehearsal of the experience.
So you are always in the position of appreciating anything aesthetically, as long as your imagination is up to the challenge. Sure you need neutral or negative aesthetic experiences to be able to contrast, but those experiences are not fixed on a natural scale, because they don't have a an intrinsic (metaphysical?) aesthetic dimension. You can revisit the experiences and create new contrasts and new scales, also based on the present moment, memories, historical contest and so on.
So I think there is always a possible mind in which a given experience can be reharsed as aesthetic. From this point of view, it's not fundamentally wrong to say that you can "cherish everything". But if there is someone here who actually studied aesthetics and wants to demolish my intuitive arguments... that'd be great.