No, the gold mining analogy is a good one: you have to do real work, and the results diminish over time as easier deposits get extracted.
You're over-thinking it because that of course is not quite right, but that's the nature of analogy.
But most importantly, this is an abberation: the final state of Bitcoin matches neither the mined nor the discovered analogy. It's all block space market.
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True. The gold isn’t manufactured. But its rate of discovery is a function of technology and demand. Bitcoin’s is pre-set. That constantly trips people up when they think of mining. Dhruv’s way of thinking about it is better. The network already has the bitcoin: they just haven’t sold them to the miners yet in exchange for hash.
The term "mining" actually seemed to have actually smoothed funding for Bitcoin mining from traditional mining investors: it's a commodity where you spend on infrastructure up-front with unknown returns which depend on market factors outside your control.