I believe PoS could be used to raise the cost for an attacker further. To date all the concepts I have sketched out have limitations I a find unacceptable but I believe there is a solution. Imagine if someday the hardware cost to attack the network was $5B but it also required another $50B in stake as well.
Here you are admitting that Bitcoin as it stands has a significant weakness.
Of course bitcoin has weaknesses, to date very little modelling of how bitcoin really works economically has been done. What happens if huge transaction fees (>1000BTC) are sent to the network, what happens if you convince 50% of the network to lease you their miners at double the market rate and what happens when market influenced transaction fees dominate the block rewards.
Bitcoin is based on the assumption that no one would ever lease out hashing power because it is always beneficial to reap all future returns rather than take a short term gain where an attacker could harm the network and perform a double spend. But people do lease out hashing power because they believe that attackers won't be able to lease out 50% of the machines and perform an attack. (Is that a valid assumption? How do we tell how many machines are currently used by attacking parties?)
An attacker with 10,000 BTC could hire enough hashing power to perform a double spend for lets say 1000BTC (probably a lot less than this in reality if miners didn't mind leasing you hashing power), the other 9,000 BTC can be double spent such that the attacker ends up with 9000BTC of cash/goods/services and 9000BTC of bitcoin. The attacker has increased in worth by 8000BTC, the miners on average have increased in worth by (1000BTC - work done producing orphaned blocks) and a lot of merchants/exchanges/service providers are out of pocket by 9000BTC.