Fishing line breaks down and loses strength if exposed to direct sunlight for prolonged periods. It is also stretchy so won't tighten round the bat when glued like a twine binding. The fishing line will naturally loosen over time as it loses it's integrity due to the sunlight.
Lastly it's abrasion resistant when wet. It's not designed for impact resistance, so could snap if you hit a ball on the binding.
In short I don't think fishing line would be suitable for bat repairs at all.
Yours
A fisherman