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.