A third quarterback on a roster should almost always be a young developmental player with upside. There are usually only two quarterbacks active on game day. That means the number three guy will work exclusively in practice. It isn't worth spending practice time on an older player who isn't seeing game time. Usually an oldish player buried on the depth chart isn't very good and never will be.
With that in mind, it makes little sense for a team to carry a third quarterback unless there is a developmental player with appreciable upside. At this point in the preseason it is unclear whether the New York Jets have one. There are two young quarterbacks, Matt Simms and Tajh Boyd. Neither might be worth a roster spot, though. Simms has a million dollar arm but only marginal upside. He wasn't even a productive college player. If you aren't good enough to play well in college, odds are you will never be a good pro. He puts no touch on his passes, and when his first read is covered seems to throw the ball as hard as he can to the next player he sees. Boyd has reportedly been an interception machine in training camp, and his 1 for 5 showing in Saturday's game was consistent with that.
There is no law a team needs to carry three quarterbacks. If one of the top two gets hurt the team can always sign a third guy off the street. For the Jets it wouldn't be much worse than turning to Simms or Boyd. If there is ever a situation where the third quarterback needs to see appreciable playing time the season is likely lost. Situations like A.J. Feeley providing the Philadelphia Eagles steady play as the third guy happen once in a blue moon. A third quarterback isn't on the roster for now.
Consider this. Many teams don't have one good quarterback. The backup quarterback market is so bleak that many people consider Mark Sanchez one of the top backup quarterbacks in the league. So if a lot of backups aren't even as good as Sanchez, think about what it means if a player isn't even good enough to be a backup.
The third quarterback spot comes down to this. A team either has a young player to develop in practice or it doesn't. It does not seem like the Jets do at this point. That roster spot would probably be better used to keep and develop one of the young guys standing out in the fourth quarter of the 2014 preseason at another position.