Also, isn't that line about 3 times too short
Nope...they are belly hooking. Certainly in the US, we either put it on the belly hook or a minimum 50ft, (typically 100 ft) line. This keeps it out of the tail rotor---either too short to reach as in the belly hook case, or with minimum 50ft the weight keeps it out.
Different agencies and/or pilots have different views on which is best. For example, CalFire does everything on the belly. USFS, DOI, BLM etc leave it to the pilot to decide most times.