What are pros and cons of Tendermint?
I'm the author of the paper.

PoW mining may be wasteful, but it's a great distribution mechanism.  Coins and other applications that use Tendermint might want to tack on a distribution mechanism that tapers off over time.  I'm also exploring alternative distribution algorithms that don't require PoW, but for now I'm busy implementing core Tendermint.

Dogecoin could adopt it with a hardfork.  Alternatively, one could take Dogecoin's transaction data and create a new coin using Tendermint's consensus protocol.  The biggest problem with this is that exchanges and wallet services may benefit unfairly.