I would also prefer season long captains, but why not combine the concepts? One offense, one defense, and one team vote each week (An MVP from the previous game?). The system Rex uses seems to be pretty weak - and only serves to elevate perhaps one persons motivation, when they face their old team or visit their hometown.
The tough part though would be... who? If one offensive captain is named, its nonsense to nominate Tyrod at such an early stage, and since Fred is gone, who on earth would you select?
Conversely, on defense, there seem to be many leaders and would be tough to select just one - probably Kyle right now?