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One of my clients used to have 'View on Staging' and 'View on Live' buttons on their ribbon toolbar and in the right-click context menu.
Whilst 'View on Site' replicates this, and provides a nice approach to greying-out the targets that are not available (i.e. the item hasn't been published to that target), the client liked the convenience of being able to browse to the published page (with fewer clicks) directly for the ribbon toolbar and context menu.
My suggestion would be to update the CME GUI to add these options in (or make them configurable). This would also make it obvious where (i.e. which targets) an item was published to.
