Wrapping cord around tool handles is a good way of improving their grip. It needn't be para-cord, any synthetic cord with the right characteristics will work. Polyester and nylon are good. Polypropylene, very prone to abrasion and UV damage, and Dyneema, tough as iron but slippery, not so much. Any middling two to five millimeter utility cord will serve. For smaller tools braided mason line can work well.

In Florida, land of heat and humidity, cord wrapping handles can improve comfort and function. But you also have to be careful. If the tool handle is prone to rust cord wrapping can hold salty sweat against the vulnerable steel and cause corrosion.

Also, IMHO, handle wrapping is not a particularly attractive way of carrying cordage. Yes, it means you have some cord, assuming you haven't lost the hatchet, but so would stuffing a hank of line in your pants or jacket pocket. And a hank in your pocket doesn't require it to be unwoven before use and, an important point in my book, the stuff in your pocket hasn't been riding exposed to the sunlight and the sort of physical abuse hatchets and such tools get.

Having some light line at hand is good. But it is better if you can break it out quickly and if it isn't half worn through or weak from UV damage.

A thirty foot hank of light line tends to disappear if you coil it loosely.