Just to get the full understanding: Only to freeze fast moving subjects which need shorter shutter speeds than the flash's burning speed HSS is really required?

Sort of. That is a common reason to use HSS, but there are also other use cases where HSS may be preferable to using ND filters.

• When you also want to use narrower apertures interspersed with wide apertures during a shoot and don't have the time to add/subtract the ND filter(s) between different aperture settings.
• When the subject is static but other things in the background are not. Think about things such as leaves on trees or wind chimes on a porch that are in the frame with your portrait subject during a windy day. The short exposure time (Tv for "time value") will freeze things in the background that may be distracting if they are blurred even if your static subject is not.

It also depends on exactly how short of an exposure you need. HSS loses more power for a shutter time of, say, 1/8000 than it does for 1/1000. It may be more efficient to use ND filters and get brighter flash output to freeze the subject with a slower Tv than to use lower powered flash output at very short Tv without an ND filter. Where the "crossover' point is depends on how bright the ambient light is compared to the total flash power available.