I do wonder if there's a way to reuse engines without reusing whole rockets, that could wind up cheaper. Pop the engine out of the rocket with some small fuel tanks, spin round and do a retro burn, then ... somehow land. I have not worked out all the details.
I'm not sure how leaving the rest of the booster would make a propulsive landing easier. It seems like more complexity than just leaving some fuel in the tank, for less benefit. But ULA's Vulcan (which incidentally uses the same BE-4 engine as New Glenn) plans on using a helicopter to catch it's engines as they parachute down [1]
This concept is generally known as "Stage-and-a-half", and it was used on the Atlas rockets
As Diane Rehm once lamented on her radio show about two decades ago, as she was interviewing some cutting-edge engineer about his work, “why does it have to be so haaaard?!?”
ULA calls this "SMART reuse" but has not yet successfully achieved it with their Vulcan rocket.
https://planetary.s3.amazonaws.com/web/assets/pictures/_2400...
In some ways this is simpler, but in others it is more complex since you need a way to catch the engines before they dunk in the salt water. A rocket booster that is already set up with avionics, engines, and fuel can guide and land itself without needing a precise helicopter catch etc.