The first and most important reason for not using PoW (proof of work) consensus algorithm is simple: DPoS (delegated proof of stake) allows implementing block lattice with all the ensuing benefits. Block lattice simply would not work with PoW consensus because it is too slow.
The second important reason is forks. Typical blockchain network can function properly when only a single chain exists. Blockchain fork is a situation when two or more blocks are pointing to the same previous block in the blockchain, creating multiple blockchains.
In blockchains with PoW consensus, a temporary fork can be created as a result of competition between the miners. More powerful miners can mine a longer chain of blocks “offline” and then broadcast it to the network. Since the longer chain wins, the current shorter chain becomes invalid along with all transactions included in its blocks. This is the main reason instant confirmation is impossible on PoW blockchains - you never know there are other versions of blockchains that may replace the chain you think is legitimate. Also, a fork can be a result of double-spending attack when an attacking miner creates two transactions trying to spend the same transaction inputs twice.
In block lattice with DPoS consensus, there is no PoW miners competition, and each client account maintains its own blockchain. Therefore, there is only one reason for a fork - when the fork is created by the account owner, intentionally (trying to "double-spend") or occasionally (software error). In this case, the network simply retains the transaction (block) that receives the supermajority (⅔+1) of approvals from the authorizers. The (legitimate) authorizer cannot authorize two transactions pointing to the same previous block, so one of those transactions will be always rejected. Note that if the blocks are created simultaneously, there is no guarantee which transaction will be authorized first.
In addition, unlike PoW blockchains where miners can mine several blocks offline, DPoS block lattice does not allow to add a new block to a block that was not authorized by the network.
The bottom line: in Lyra DPoS block lattice, a temporary fork can only be one block long, exist just for a fraction of a second, and affect only a single account/block/transaction. This condition enables instant and final transaction approvals and prevents chargebacks. That’s exactly what the payment industry is looking for.
Another important reason for not using PoW is often overlooked but very familiar for blockchain developers: DPoS eliminates the costs and risks of frequent hashing algorithm changes, testing, and mandatory network updates required to keep up with changes of mining hardware and software. When new mining hardware such as ASIC or graphic card becomes available to a small group of miners, or becomes too cheap to rent, it enables hashrate attacks on a PoW blockchain. Developers must frequently adjust their hashing algorithms instead of working on product development.
And last but not least, another reason against PoW is DPoS eliminates an enormous cost and waste of power caused by mining, which is even more important for constantly growing number of people around the world than everything listed above.
A major advantage DPoS consensus algorithm over Proof of Stake (PoS) is that in DPoS your vote works as a DeFi staking for you - the same way as supernode or masternode staking works in PoS, but you don’t need to host and maintain the node. There is no need to run an authorizer node, just vote for the authorizer you support and get a share of their revenue. So the hard work - hosting and servicing the authorizer nodes - is done by skilled people with significant resources which ensures the fast uninterrupted network service. And at the same time even a larger group of people, who still want to be an important part of the project but cannot or don’t want to work on it full time, can become the network stakeholders by simple voting.