The rumors flying out of the Jets locker room for the past year has been that Sanchez has a poor work ethic in practice, which ticks off other players. So bringing in Tebow is not going to ruin any team chemistry. However, this does appear to be an attempt to push Sanchez, especially since they just extended Sanchez' contract. They didn't give up much for Tebow, so he is the one who is expendable.
Jacksonville was definitely a better fit, and I am quite surprised that the Jaguars did not offer more than a 4th-round pick. Tebow's contract seems to have been the problem ($5 million clause for the Broncos, seriously?). I wonder if Tebow himself knew that his contract said that. Still, the revenue that Tebow's presence would have brought to a Florida team would have easily exceeded $5 million in his first year.
In the end, for that kind of clause money, there weren't many teams that could afford to pick Tebow up. All the other teams with that kind of money to spare already had franchise QBs.