You misunderstood me. Of course a renovation improves the value of something, but it is not the cost of the renovation which provides value, it is the resulting product - the production - from which the value is derived. Stated differently, if Renovator A spends $100k on a project, and Renovator B spends $50k to get the same results (through more efficient sources and means), the buyer is not going to offer Renovator A more money just because that work costs more.
The buyer of a renovated property cares nothing for the cost of said renovation. He cares only (or should care only) for the resulting product. How such product was achieved is irrelevant to the buyer. There is a caveat... in those cases where learning the costs DOES induce a buyer to spend more, it is because he has learned more about the final condition of the thing by learning of the cost. But one should not confuse this with him caring anything for that cost itself.
Case in point: say you're selling me a used car. I offer $10,000 for the car, based on my assessment of its condition, etc. (Assume I am pretty knowledgeable in cars and can make an accurate assessment). So I offer $10k. If, after that offer, you then divulge to me that you had to spend $8,000 in order to get the car to that state, I will not change my offer if I am a rational buyer. Your costs are irrelevant to me. All that matters is the resulting product - I assess and bid on that thing alone, not the consumptive cost of resources which went into it.
The relevancy for Bitcoin should be clear: a buyer of Bitcoin (if he is rational) should only care about the usefulness of the coin itself, or if he is speculating then he cares about the usefulness to someone else in the future. He cares not at all for the costs of the miner's time, or his burden of equipment.
This is why it is false to say Bitcoin's value is "backed" by the cost and burden of mining. Try to sell some hard-earned sea mud and you will see quite quickly that your costs and struggle are irrelevant in the final bidding price.