This is an amazing guidance and control capability.
I can’t imagine it’s use, as it requires so much propellant weight to first boost and then land the craft.
It would effectively cut the throw weight of the vehicle in half.
The vehicle is far lighter when it's time to land it than it is when it's launched, since most of the fuel has been used, so it's not "half" - more like 30%. But if you can launch 140% of your original throw weight in two launches by simply refitting and refueling between them, when fuel is 0.3% of the cost of the rocket, instead of building a brand new rocket for the other 40%, then you're far, far ahead of the curve. We don't throw away 747's after every flight, and a rocket costs about as much.
Yes, but you have a reusable vehicle, instead of throwaway stages.