Whoa, you are very, very wrong to think you don't have to pay taxes on crypto. I won't speak to other countries, although I do know they have tax laws that effect crypto, but in the US you must file capital gains tax for any crypto holdings you buy/sell/trade.

I think what you're really trying to get at is that crypto can eliminate the middle-man who takes a cut. While this can be done, there's many times when middle-men are still present in crypto too.

One example is decentralized exchanges using the 0x protocol. The trustless trade of one token for another at a certain exchange rate can be done without a fee, but decentralized exchanges acting as transaction relayers are providing a service at a cost, so they should and do inject a fee into these transactions.

Is gas in fact some sort of tax/incentive payed not to bankers but the whole network of miners who agree to keep record of everything(i.e. mine)?

Gas is the scaling factor that makes the fee proportional to the computational work done, not the fee itself. The fee is paid in Ether.

This fee exists to prevent people from attacking the blockchain and to incentivize miners to maintain the network. If you didn't pay miners, then they wouldn't mine and you wouldn't have a blockchain.

Proof of Work consensus is it's own thing. It can be applied to blockchain technology, and most blockchains do use it, but it is not limited to this one application. PoW has a lot more to it than just fees & computers doing "stuff".