As always, I lean on the excellent NYJetsCap.com to look at potential ramifications of any move. That site is a must read for any armchair general manager. Taylor has another year left on his deal at $2.275 million. Cutting him would leave the team with no dead money so the Jets would get his entire contract in cap savings.
That is not a ton of money, but it could add up to a reasonably priced starter. For reference, Sione Pouha, Mike Devito, and Jim Leonhard are all in that range. The Jets could use that money to go in a lot of different directions, but freeing up that kind of cash could get the team something decent in return in the mold of the guys mentioned above. The team could also use the savings to spend on keeping one of its own free agents.
There is also the possibility that Taylor might take a paycut to return to the team. He is another one of those guys at the tail end of an outstanding career. The only thing he has left to chase is a ring. Even a minimum salary might be more than he could make doing anything else.