The reason for compensating miners (with fees, subsidy, or anything at all) is that because in a PoW scheme they provide a service that is vital to the entire market.
In a scheme where solving progressively complex cryptopuzzles does not serve to secure the ledger against doublespends and other shenanigans, mining is, frankly speaking, a waste and should have been replaced with a more reasonable initial wealth distribution routine - of which there are many options (including collusion-proof cryptographic lotteries)
In fact, mining provides outright perverse initial wealth distribution in pure PoS because you are essentially rewarding folks for the investment they have made into another, different crypto-currency scheme (by buying BTC mining equipment), an investment that has been likely already paid off via that other scheme.
That's like if Microsoft started paying me money for the fact that I own Google shares
In a scheme where solving progressively complex cryptopuzzles does not serve to secure the ledger against doublespends and other shenanigans, mining is, frankly speaking, a waste and should have been replaced with a more reasonable initial wealth distribution routine - of which there are many options (including collusion-proof cryptographic lotteries)
In fact, mining provides outright perverse initial wealth distribution in pure PoS because you are essentially rewarding folks for the investment they have made into another, different crypto-currency scheme (by buying BTC mining equipment), an investment that has been likely already paid off via that other scheme.
That's like if Microsoft started paying me money for the fact that I own Google shares
Interesting point, and I agree with the wealth distribution argument. However this can be fixed by not using SHA256 which is not designed to be a technology-neutral algorithm.
Well, yeah, a different PoW might have alleviated the issue a bit, though designing a PoW that would be hostile to modern mining equipment turns out to be a pretty hard task it seems...
Regarding a crypto lottery, where is the collusion-proof cryptographic lottery that is immune to a sybil attack?
Immune ? No.
But significant sybil-resistance could be achieved by various tricks (an obvious and somewhat imperfect one would be to use v4 IPs as "identities". Admittedly, you can still sybil a lot, especially if you are a botty op, but during initial wealth distribution a botnet is not likely to show up and anyone who honestly buys a crapton of IPs just to win MORE PPCOINS is probably an individual with quite a bit of interest in your specific coin)
