If you are simply mining bitcoins and don't sell them or trade them for anything, then there are zero tax implications.
I don't agree. If it's a business, you have business losses (equipment depreciation, electricity, and so on). If nothing else, you can file them and carry them over in case you make a profit in the future. If it's a hobby, you'll have hobby losses. Again, if you don't file them, you can't use them to offset your (you hope!) future profits when you sell those Bitcoins.
If you have gains from other activities in the same category, you can usually use the losses to offsets gains from other activities. For example, if you are a self-employed consultant and mine Bitcoins in the reasonable hope of making a profit, every dollar you spent mining is effectively one dollar you didn't earn consulting. (Not counting capital expenses which you have to depreciate, but that's still better than nothing.)
It is like digging up shiny rocks (or gold) in your back garden and storing it in a safe place inside the house. But even more nebulous, you are finding special digital patterns on the network, that may or may not be valuable to others, and storing the output on your electronic equipment.
Exactly, and it costs you money to do this -- costs you have every right to offset against future profits .. *if* you report them.