That has been repeated many times but is not true, the price of an arbitrary unit of currency or crypto has no relationship to its security. That price going up or down has no relationship on the "security level" of the blockchain.
To me, it seems that as the value of that ether increases, they have more incentive to behave, rather than risk the loss of their investment + large capital gain.
Consider the reverse, the exchange rate for USD to ETH is one one hundredth. So the stake is just 3,200 eth, and again, same thing.
Let's say hypothetically one eth was worth about a Satoshi, 0.05 cents or so. So they could just require 1,000,000 eth as a stake. Or ten times that. Or a hundred times that.
It's irrelevant what the price is, the choice of the stake amount is. If eth was inflationary, they could inflate the stake proportionally.
They could choose to require one gwei, one ETH, or one million ETH. That's your protection. The exchange rate from USD to ETH is irrelevant.
> The exchange rate from USD to ETH is irrelevant.
Unless the attacker already has a large enough portion of the Eth supply to execute an attack, they'll have to pay to acquire it.
[1] 1/3 voting power would theoretically let an attacker double spend by getting two conflicting forks committed; 2/3 would let them commit invalid and/or unavailable state.
I think you may be misunderstanding staking. Your vote is proportional to how much ETH you stake, it seems like you are picturing everyone gets 1 vote. The only reason for the minimum stake amount is for performance reasons
3,491,906 ETH is currently staked right now which is actually way lower than will eventually be staked when PoS goes live later this year. 33% of this is 1,152,329 ETH which at current prices of $1,776 puts a minor attack at over $2billion. This is without considering that after the attack the network could easily fork and remove the attacker's ETH from existence so it's hard to see economics working in the attackers favor.
A high price of ETH means it costs an increasingly astronomical amount to attack the network and pretty much no way to do it profitably.
Well, there wouldn't be much point in attempting an attack if the attacker didn't have the ~1/3 voting power to successfully execute it, right?
Also: People stake ETH under the expectation that the ETH they generate are worth just as much or more as the ETH they staked. If the price would continuously go down, less and less people would stake. The less people stake, the easier it is to buy 1/3 of voting power.
On the other hand, the higher the price of Ether is, the higher the incentive to do so. The return on investment of an attack is independent of the price of Ether (assuming one can actually gain something from attacking a POS chain).