There was no legitimate reason to carry Burnett on the roster save to spare the psychotic hurler's very expensive feelings. If Burnett had gotten into a game on the Division Series' planned schedule, that would have meant the Yankees were getting blown out -- in which chase, who cares who pitched?
But, as 24 different games this year have shown, rain was likely to impact this cold-weather series. And the Yankees were caught with their pants around their ankles when Mother Nature came a-knockin'. If a game were rained out (which happened), or if a starter got injured (also possible), the team knew they'd need a fourth starter. Yet they didn't carry Bartolo Colon, who was significantly better than Burnett all season.
You'll hear a lot of justification about how Burnett was good down the stretch, but if you look at Fielding Independent Pitching, he was no better than the rest of the season. He basically pitched one good start against Boston in a meaningless game the last week of the season. The rest of the 162-game schedule, the guy was a walking, blond gopher-ball machine. And now he might decide the fate of the season.
There is no excuse for this kind of poor planning from Joe Girardi and Brian Cashman.