Great work.

I hope and believe that some kind of POS have to be done.

"Recall also, that the necessary proof-of-work investment is much smaller than the proof-of-stake investment."

Does this not depend on whether the coin is Bitcoin or an Altcoin.

"At the same time, the attacker faces costs related to losses on bitcoin-specific investments which are necessary for the attack. It can be assumed that a malicious attack causes the purchasing power of bitcoin to fall to zero. Under such an attack, the proof-of-stake monopolist will lose his entire investment. By contrast, a malicious proof-of-work monopolist will be able to recover much of their hardware investment through resale"

This implies that when it becomes necessary to use ASIC in order to mine bitcoin, those ASIC investment will be a kind of, proof of stake,
if they can´t be resold after a Bitcoin attack unless its just a matter of a simple change of a chip.

Ofcourse real POS rules would also mean an economic loss of the loss of value of coins owned.