How do you fix the past?
If someone had 51% of a Proof Of Waste coin's hash power, what can you do to prevent him forking the chain?
The same way as with Proof of Shit coins. So why are we discussing this aspect?
Duh. I was making fun of your question as any decentralized consensus algo is vulnerable to some type of 51% attack.
DPoS
We are discussing PoS versus PoW here, and why people support PoS specifically.
So.. you are going to cherry pick the version of PoS that best fits your argument? DPoS is PoS, it is just a variant of PoS. There are many PoS variants and people all too often wrongly refer to them as all having the same pros and cons. Misinformation on PoS is spread in an echo chamber around here.
You would need to buy up 51% of the currency supply to use this attack vector.
Just as it happens for many coins an exchange owns more than 51% of the supply. They paid NOTHING to obtain it. You are entrusting them directly (or indirectly when they get "hacked") to not fork your coin.
Provide proof 51% of the currency supply of any PoS coin are on centralized exchanges. This seems like a wild claim that you cannot back up and I wouldn't be surprised if it is wrong. Volume on all coins is split amongst exchanges so this risk is mitigated, even if 51% of the currency supply did happen to be on exchanges (which it isn't.)
Let's consider Proof Of Waste for a second. 51% of Bitcoin's hash power is on 2 to 3 mining pools. The paid NOTHING to obtain it. You are entrusting them directly (or indirectly when they get "hacked") to not fork your coin. By the way... this statement I can back up with facts and readily available data.

See how dumb this argument is? Proof Of Waste supporters grasp at straws all day every day. Yes, PoS has vulnerabilities,
but so does Proof Of Waste. PoW supporters ignore its vulnerabilities when talking about PoS as if its shit doesn't stink, when in actuality a lot of the arguments they make can be applied to PoW.