A toy paper kite will tear up in too much wind. The flimsy cotton string used will break easily and is not prone to rope burns, slicing wrists to the bone or popping off fingers at the joints. The flimsy spars of the dimestore kite will snap easily if overstressed. Thus it is relatively safe to fly such a kite. A kite made of ripstop nylon, carbon filament spars and flown with heavy duty nylon cord is a very different item that must be respected.
Rope burns can happen quickly and cut to the bone or worse.
Hand protection is mandatory. Rope burns are terrible. It is well worthwhile to invest in a small parafoil or winged box kite suitable for 40 or 50 pound line and test fly it to get a feel for heavy duty kites. Remember, a kite twice as large is going to have a pull four times as great or more. The large military kites were flown from special trucks that carried large drum wenches.