The thing that is mined is just very long numbers. It is difficult to find them, even if using special computers. You cannot find them with a regular PC anymore. This labor (such as investment into the equipment, and then expense of electric energy) is called "proof of work." Once you mine your Bitcoin, it then represents the resources that you spent on producing it. The difficulty of mining is adjusted periodically, so that it keeps up with the costs. So in the end a miner exchanges his electric bill for the Bitcoin. He then can expect that his Bitcoin has value - roughly as much as he spent, but in reality only as much as others are willing to pay for it.
The Bitcoin, indeed, has no inherent value. Many currencies are like that, so that's not unique. Only commodity money has intrinsic value; the rest (representative, fiat, coins, paper bills, bank papers, and electronic) are made as cheaply as possible. Bitcoin is an outlier here - its coins are expensive because that's the only thing that stops a random person from minting a trillion of those. This is one of the problems with Bitcoin, as miners have to waste perfectly good electrons to calculate long numbers that are of no value themselves, outside of their use in the Bitcoin network.
Comparison with tulip bulbs is not unreasonable. In both cases the items are acceptable tokens that represent some amount of something that has value. Bitcoin is a valid, mostly secure (in theory) electronic token. Only a few problems of Bitcoin are related to its nature, such as the need to use a computer and be fluent in bitcoining.
Bitcoin has no inherent value, as opposed to cost. (You can spend a million dollars doing useless work, for example, but nobody will buy your product - so its cost is larger than its value.) The value of a Bitcoin is softly limited on the bottom by costs of mining it at a given time. There is no limit at the top - people can trade it at whatever they want. A Bitcoin holder may "sell" his coins from his left pocket into his right pocket, for a million dollars each... and this will help establish the exchange rate for others. Ways to play the exchange are known since the first stock exchange opened (probably somewhere in ancient Egypt.) Intentional and unintentional (but still cascading) forces can be applied to the market, resulting in the Tulip bubble and the South Sea bubble, and the Housing bubble. Bitcoin is not safe from being pumped and then dumped - people who are doing this are not computer scientists who are fascinated with cryptocurrencies. It is done by experienced FX operators who can't care less what the currency is, as long as they can buy it low and sell it high. The early adopters of Bitcoin, who are now sitting on the unrealized wealth of about 1/3 of the planet's worth (if Bitcoin becomes an accepted currency,) have no objection to that.
If/when the cost of mining a bitcoin exceeds the "value" of generated bitcoin for some extended period of time, the fallout — the "bear market" in Bitcoin (and/or switch to mining other cryptocurrencies such as litecoin etc., potentially with the process repeating itself a number of times before it will be declared a pyramid scheme) — will be swift and cascading.
The early adopters of Bitcoin, who are now sitting on the unrealized wealth of about 1/3 of the planet's worth (if Bitcoin becomes an accepted currency,) ...
I think there may be a problem with your estimate. At the "guaranteed" limit of BTC in circulation capped at 21 million and assuming 1 BTC is trading hands at USD$1,000 (which is more than double of current conversion price) the total capitalization of entire Bitcoin economy would amount to USD$21B (at most, counting bitcoins that are lost, "unminted" and hoarded - IOW, not in circulation) — a piddly amount of international trade - about a quarter of current annual revenue of Amazon, about 2/3rd of American Express annual revenue, or about the combined annual revenue of Visa and Mastercard. **
Of course, if we assume exchange rate of 1 BTC per USD$1,000,000 then the [eventual nominal] Bitcoin economy would approach USD$21T, or approximately the size of entire US economy in a not too distant future. *** / ****
Of course, synchronizing the ever-growing distributed blockchain database will inevitably slow that "economy" down significantly (yes, I know about "light clients" and "pruning" - good luck doing that in real time in a multi $Trillion economy with millions of transactions daily, without compromising and jeopardizing transactions' security) - the decentralized system of making Internet micropayments simply was not meant to be that scalable. In other words, there are a lot of serious technical and nontechnical disadvantages in the decentralized / "communal trust" scheme, not just ephemeral "political advantages" over other fiat currencies the Bitcoin faithful are emphasizing.
There are far more robust secure digital e-payment systems already on the market, and more are coming. And none of them have the "currency" or "investment" risk or elements of pyramid scheme present in Bitcoin.
Also, the Bitcoin proponents like to favorably compare the cost of Bitcoin transactions with the credit card costs, but they ignore the costs of conversion into dollars or other fiat currency, and the fact that the credit card charges include the credit risk (since in reality it's actually a loan / credit that defers the payment) while the debit card and Bitcoin don't extend credit and therefore should be significantly less expensive to process - as the debit cards are. Turns out, Bitcoin should be compared to the debit card, and it is not a cheaper way to pay for "stuff" once the credit risk is taken out of the equation. *****
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** Ref: Bitcoin is Gold 2.0: But how can it be regulated? - FR, post #22, 2013 December 28
The Serious Disadvantages of Bitcoin - FR, post #21, 2014 January 05
***
Currently there are more than 12 million bitcoins in circulation, so total potential Bitcoin "market" capitalization will be significantly smaller than "potentially authorized" capitalization. At the rate of creating approximately 25 bitcoins per 10 minutes, it would take over 100 years to create the [complete] supply of 21 million bitcoins.
**** The bitcoin value forecasts from wiki: Financial journalists and analysts, economists, and investors have attempted to predict the possible future value of bitcoin. Economist John Quiggin stated, "bitcoins will attain their true value of zero sooner or later, but it is impossible to say when."[93] In 2013, Bank of America FX and Rate Strategist David Woo forecast a maximum fair value per bitcoin of $1,300.[104] Bitcoin investor Cameron Winklevoss stated in 2013 that the "bull case scenario for bitcoin is... 40,000 USD a coin".[105] In late 2013, finance professor Mark Williams forecast a bitcoin would be worth less than ten US dollars by July 2014.[106]
***** Ref: Bitcoin Is an Expensive Way to Pay for Stuff - FR, post #21, 2014 January 05
Debit vs Credit Card Charge / Offline Debit Vs Online Debit Vs Credit Card Charges - Cardfellow.com, by Ben Dwyer, 2013