Cryptocurrencies give us the opportunity to digitally control our own money and really own it instead of being dependent on banks that operate on fractional reserve.
That's enough reason for its existence.
I agree except please note that Satoshi's proof-of-work will unavoidably end up (probably already is) controlled by a cartel of miners who can censor your ability to transact. Imagine they are bribed to exclude you. Or
the coming world finance government (e.g. IMF, World Bank, SDRs replacing the dollar as the global reserve currency) regulates the miners and dictates who can and can't transact. At the moment, this developing cartel is not focused on censoring you, but rather on gaining a monopoly on transaction fees, so that they can raise their income to the maximum that the market will bear. This is the politics around the blocksize debate. I wrote in great detail about this in my coming whitepaper (excepts have been published to these forums already). Any entrenched centralized control ultimately ends up being co-opted by the State and
the political power vacuum of collectivism. We have 1000s of years of human history without any exception!
So it is not enough to say we control the private keys. We must also have a global ledger consensus which is impervious to centralization. So far, neither Satoshi's Proof-of-Work (PoW), nor state-of-the-art alternatives such as Bitshare's (Steemit's) Delegated Proof-of-Stake (aka DPoS, combined with Transactions as Proof-of-Stake (TaPoS)), avoid the centralization of control of the global ledger consensus.
As I have alluded to, I believe I have a design alternative which provides a solution to this fundamental problem that has been plaguing society since time eternal.
Concerning Bitcoin POW winner takes all argument, I can tell you there won't be any system that will be 100% without any flaw.
Life requires flaws. It is precisely flaws that make us unique and alive. If everything was predetermined (flawless), then nothing would exist. The past and future would collapse into indistinguishable (the light cones of special relativity would collapse onto each other). Life requires that real-time omniscience is impossible, which is a conceptual analogy of flaws (i.e. that not all of our actions can be congruent always in real-time).
However what we are talking about here is not attaining "perfection" (not attaining holistic congruence), but rather how to have a system which has some ordered state of equilibrium which is not trending towards Coasian costs maladaptation implosion. In other words, we want a system with maximal degrees-of-freedom. The flaw of PoW and DPoS is they lack degrees-of-freedom because they depend on the economies-of-scale control of some finite resource (mining or stake).
Thus, I believe there can be a design for global consensus which has a form of decentralized equilibrium.
Please read
my summary of altcoins.