MAC protocol with throughput of 1
There can be many reasons, but one example would be fairness. Suppose you have a modified version of ALOHA where one priority user has transmission probability set to 1 and all others to 0. Assuming the priority user always has a message to send, this scheme has a throughput of 1. However, this is an awful scheme if you care about any of the other users, because they are going to experience infinite delay.
This is why researchers often prefer working with network utility functions as performance metrics to account for the welfare of the network instead of just overall throughput.