The main argument is that balanced (proof-of-stake + proof-of-work) system is self-sufficient while (proof-of-stake + auxiliar proof-of-work) doesn't provide a self-sufficiency because it depends on stability of auxiliar chain. So we have to keep a support for native proof-of-work along with auxiliar proof-of-work to keep self-sufficiency.
This solution sounds simple but it's impossible to implement a sustainable proof-of-stake + native & auxiliar proof-of-work system. It's impossible due to self-competition between native & auxiliar proof-of-work miners.
Why self-competition isn't a good thing? It's quite simple, just one example:
PoS -> PoS -> PoS -> PoW -> PoS -> PoS -> PoW -> PoS
vs.
PoS -> PoS -> PoS -> PoW -> PoS -> PoS -> AUX PoW -> PoS
vs.
PoS -> PoS -> PoS -> AUX PoW -> PoS -> PoS -> PoW -> PoS
vs.
PoS -> PoS -> PoS -> AUX PoW -> PoS -> PoS -> AUX PoW -> PoS
Which chain should be preferred? It's obvious that auxiliar proof-of-work difficulty will be higher than native proof-of-work difficulty, so the last chain will be selected. But this solution is flawed because it makes native proof-of-work blocks less secure in comparison with auxiliar proof-of-work blocks i.e. malicious auxiliar miner will be able to fork native blocks out of the main chain*.
There is no way to calculate correct trust for so heterogenious chain. We can calculate a trust score for proof-of-work and native/auxiliar proof-of-stake blocks, but we can't make a correct difference between native and auxiliar proof-of-work.
Of course, we can fix a trust of auxiliar proof-of-work blocks at 1 or use another value but it makes no sense. Because such blocks wouldn't be able to provide any security into the block chain and native proof-of-work miner will be able to fork auxiliar blocks out of the main chain (direct opposite for * scenario).
So, we can't implement a sustainable PoS + PoW + AUX PoW system with separate aux and native difficulties. We have to use equal difficulties or remove native PoW to make PoS + AUX PoW design reliable.
P.S. I guess that beta implementation of coin mixing protocol will be ready for testing in the near future.
