If you assume that market participants only buy sandwiches with the most slices then no competitor can produce sandwiches with unapproved vegies or meat.
The purpose of the POW is so nobody can fake transactions. Cryptocoin is an attempt at solving the N-thieves problem. This is similar to the Byzantine Generals problem. You're fixated on a purely technical analysis without any concern for the fact that people have to send something that needs to maintain its value much longer than its transit time.
The purpose of POW is to make it difficult to fake transactions at great expense. With DPOS it becomes impossible to fake transactions in less than 15 minutes compared to bitcoin where it never becomes impossible without manual intervention of checkpoints.
POW destroys value in a very real sense. The goal is irreversible consensus. POW cannot give you that and is very costly.