A 28 foot run of string, assuming 14 full grown 30 pound plants, your creating around 1500 ft-lbs of torque on each post, equivalent to a 210 lb man hanging from the center. (Doing the math in my head).
You'd be much better off doing a Florida weave and also using 3 more supports with that length. Tomatoes need to be tied up as they grow or they just fall and sprawl...
A fantastic idea for beans however