What is the downside of not using Proof of Work for validator selection? Bitcoin uses Proof of Work for two things: one is to secure the blockchain with strong cryptographic signatures like a Merkle tree, and the other is to crown the validator which "mines" a solution as THE validator (dictator) who determines which transactions to broadcast in that block. If they blacklist your address (or charge large fees) and don't want to accept your transaction then maybe another validator will eventually accept it.

But why do we need Proof of Work for the second thing? What's wrong with Proof of Correctness as Ripple uses, or Delegated Proof of Stake as LISK uses, for example? Why are they considered "not decentralized" while Bitcoin is said to be "decentralized" despite the arms race that has caused a few mining pools in China to control more than 51% of the mining power in practice?

What is wrong with a community electing 101 random validators like with LISK for example? How can this be gamed to reduce people's freedom to transact or have their transactions confirmed? The worst thing is some address may be blacklisted by a few validators (eg under pressure from a government law) but the same can happen with bitcoin miners, since we know who they are. So what's the disadvantage of Delegated Proof of Stake?

Here are the advantages: less waste of electricity, faster consensus, and possibly more decentralization in practice.

If I am right and this doesn't have any serious disadvantages, it should be rather trivial to make a cryptocurrency with delegated proof-of-stake electing N (odd number) validators.
Proof of Work is needed to inventivize miners to not fork and, if there is a fork, some metric for determine which fork is the real blockchain (assuming no consensus changes in the fork).

Proof of Work incentivizes miners to not fork (i.e. see someone else's block, ignore it, and create their own block at that height) because of cost. It costs resources in order to produce a fork and stick with it. If their fork has no value, then they are wasting money on something that is worthless. However with other consensus systems like Proof of Stake, there is no cost to make a fork. Making a fork does not cost anything as there are no resources for you to spend to make the fork. In some systems, you can make a fork and still be mining/staking/minting/whatever on the original chain at no extra cost and no opportunity cost.

Proof of Work also provides a metric to determine which chain is the correct chain. Given two blockchains with the same consensus rules, the one with the most work (the sum of the difficulties of all of its blocks) is the one that is considered "the blockchain". In other consensus systems like Proof of Stake, no such metric exists for determining "the blockchain". This results in centralization as someone or something is needed to say "this blockchain is the right one". In some coins, a signer (usually the developer) must sign all blocks for the block to be considered valid, so that signer determines what "the blockchain" is and is a point of centralization.