I don't think a idea of a time-based-fee is bad but there is a major problem with deciding what it should be. I mean you can just make up any number you want, but if you are going to bless the idea what the economic holy water of eliminating externalities it should bear some relationship to the actual cost and I don't see any way whatsoever to do that. (Otherwise you are just adding an externality, possibly larger than the one you eliminated.) For one thing the actual cost depends on the number of nodes that are storing it.
As far as there being a cost for waiting longer to dig, that already exists. It's called staking and is a very large cost right now. Over time it will get somewhat smaller. A page or two back we roughly estimated it at about 4% per month. I don't know if that is actually very accurate.