A few reasons.
First off, the Jets will be trying to evaluate players for next year. Right now, I don't think Rodgers is a viable enough QB to do that with. Second, from a competitive standpoint, Rodgers is a sitting duck back behind a horrible line. Taylor has a bit more elusiveness. From a financial standpoint, why pay Rodgers more money for hitting contract incentives by playing half hearted football?
Fans a media like the "Play out the string" theory. For players, they are auditioning for a new coach/GM in New Jersey or another team around the league. They want to play well and win and get good snaps on tape.