Actually it's more like this...
The US sees it as money falling into your lap, as if you did it for free. That is because it is treated as property. Think of it like this, you "inherited" Bitcoin from your uncle when he passed away. But your uncle is a miner.
They are not recognizing that you've paid taxes on everything that allowed you to mine. And if you didn't it was probably subsidized by taxes. Yet. They do not recognize the POW required, either.
Your analogies do work. So you can see how absurd it is...
There are actually funny clauses. Technically if you don't regularly and substantially (the law's words) produce bitcoins you don't fall under the law. No one with a "hobby" fits under the law, legally. However this clearly doesn't make any sense given that there's no reason to turn off a bitcoin miner. And there is no definition of what "substantially" really means; but it would be clear if you lived off of it instead of another source of income it would be considered substantial.
Here's an analogy I will make: If I make a substantial omelet every morning single morning, do I own tax on the going rate of $12 at a breakfast restaurant?
I recommend you don't pay taxes. Frankly I cannot condone paying taxes on any crypto until the conversion to fiat. I am not saying what I suggest is defacto legal. The problem is while you could probably win in court, you can't afford to fight the battle in court. The future is unwritten in this realm. For countless reasons it's not practical at all to impose these taxes. Examples are: embedded forms of mining & fractions of unmovable amounts; the US will be crippled in financial structures by being out-competed, the state has no real purview over something that is decentralized globally & offers no basic rights for the, etc!
You can always choose to record your mining for future implications. But as you know this is basically insane as well, trying to keep track of tiny fragments of stuff.