It's not just energy that's being wasted in theory, though; it's also computing power unnecessary to the core task of Bitcoin except that it has a predictable difficulty.

It would be nice if the mining process could incidentally cause some external benefit. If we were deciding between two scarce physical stores of value (say, gold and something else), and gold requires the mining process it does today whereas the alternative requires equivalent expense and involves equivalent scarcity but happens to reduce global warming or contribute to medical research, there would be little reason to choose the former.  (The only reasons would involve the purity of the object as a store of value without any incidental worth, but there's little reason in an efficient economy to believe that that matters in the long run.)

Basically, a very simplified way of looking at it is that you have to find a particular value of n such that f ( n ) returns a desired value (you nit-pickers in the back row keep quiet! I said this is simplified). The function f is designed in such a way that changing the value of n even the tiniest bit gives a completely unpredictable result; f( 1 ) might give 33929494, and f( 2 ) might give 4. So the only way to find the value of n that solves the problem is by brute force: try each possible value of n until you find one that works. The value of n that solves the problem is called the proof of work.

The function f and the value n have an important use in Bitcoin, so the solution is not just some pretty value that gets put on the fridge for a few days then quietly gets buried in the recycling bin.

Your idea of using 'useful' calculations to maintain the rate is interesting, but I'm not that it can be worked in. The problem has to fulfill two criteria. First, it has to be something that can be dynamically adjusted to compensate for more and more computers coming online to solve it. Second, the problem must be difficult to solve but easy to verify the solution, because every client will verify the solution at least once, if not several times. And, let's face it - we're dealing with money. A lot of people will be very motivated to claim they found a solution, so we must be able to check their claim quickly and easily.

'Useful' calculations could probably meet the first criterion by varying the number of folds, or the number of digits to solve, and so on.

With the current setup, finding the solution is very hard, but checking whether the solution is correct is, comparatively speaking, trivial. If someone says "Hey, the answer is 542214675," you don't have to try all the values from 1 through 542214674 - all you have to do is plug 542214675 into f and verify that the result meets the requirements. I'm not sure the same thing can be said about folding proteins, extending a transcendental number, and so on - I suspect you would have to duplicate the entire work effort to verify its legitimacy.

and about inefficiency and wasted energy:

what amount of energy is wasted to produce the so called 'real money' ?
what amount of energy is wasted by all those security- and computer-systems that watch over the so called 'real money' and keep track of and allow transactions?
what amount of energy is wasted producing and driving around thousands of big armored trucks with armed guards to transport that so called 'real money' from Alice to Bob?

nothing real is produced by that huge amount of energy.
besides that you even pay your bank and government to waste it, how silly is that?


the small amount of energy needed to keep the bitcoin-network going doesnt even get close to a fraction of that.

Difficulty is self adjusted by the network, to keep the block generation (and therefore the btc generation) at a regular pace.
But, as total hashrate capacity is bigger, the whole network is more secure, and less likely to be attacked.

No.
The correct answer is that the whole btc network relies on the proof of work made by all the participants, including the miners.
No mining, no bitcoin network.