Putting cost into something doesn't generate value. I have an acre of land. If I hired a team of workers to repeatedly dig a hole in my land and then refill it with the dirt they dug up, my land wouldn't become worth a million dollars just because I expended a million dollars of labor doing something pointless. Likewise, bitcoins don't have value just because you expend valuable computing and energy resources mining them.
> Couldn't the real life costs of mining the coins be a base for the bitcoin value ?
Not really. You can't recover the costs by "melting down" bitcoins, so it doesn't provide a support for the value of bitcoins the way that the use-value of gold might provide a support for the value of gold currency.
Clearly, if the cost to mine coins is less than the market value plus the expected transaction fees that can be earned by mining (mining is also transaction verification), there is no economic incentive to mine, but that doesn't operate as a price floor so much as a limit on the viability of the system.
"Anything"? Yes. People aren't going to make new things at cost X with the goal of selling them at cost Y. If they did, the price would fall further, faster. Therefore, there's some relationship.
That said, it's by no means a floor, particularly on goods that stick around a while, since the things already in existence can more than meet the demand, which can drive the price arbitrarily low.
It's more like the value determines the mining cost. The coins are created at a fixed rate, and the difficulty of creating them adjusts to the total computation being spent on the task.
As the value of the created coins go up, miners can afford to spend more on the effort in an attempt to capture a bigger share.
