The rocket would keep same descent system as now (no parachute). But instead of landing on feet, it would have long grid fins on its top that would be caught by an elevated cable net.
The previous SpaceX attempts showed that the landing position is very precise, but that it's hard to land slowly and stable enough to avoid falling on its side or break a leg. This solution objective would solve this issue, plus reduce the rocket weight.
The global idea is to transfer as much as possible the landing system (and its weight) from the rocket to the ground.
- No parachutes, keep the current advantages of controlled descend targeting a precise and optimal position in the sea.
- No more heavy legs.
- Cannot fall after landing or break a leg anymore.
- The long top grid fins would help stabilize the descent, and slow down a little the rocket (opposite of the current bottom legs that makes it harder to control).
- The landing impact force would be absorbed by the elasticity of the fin (and the whole platform on water) on several meters; much longer than the current brutal impact on feet. So the rocket could land with a higher speed, saving more fuel.
So, surely there must be flaws and issues with this idea... waiting for your opinion and ideas!
EDIT: Top-view of the net below. Metal structure would be 50m wide (same as the current landing platform), the net hole 15m in diameter, and top legs 15m length, so it cannot fall through the hole nor be in contact with the solid structure.
About some very interesting issues reported in the replies:
Rocket precision to enter the net hole: the hole would be 15m in diameter, and the target precision of SpaceX is 10m, so it should be already OK.
Net would burn/melt from the rocket fire: as seen in the point above, flames should not touch the cables - and cables should be quite resistant to them anyway.
Top-Legs resistance (15m instead of the actual 7m):
I think a lot of the weight of the currently used legs which comes from the huge hydraulic cylinders required to open the legs against the air friction (not the case for that in top-legs).
Also, they need to be very strong to support the instant landing impact, that would be smoothed by the net elasticity.
We can also imagine some "legs" a bit different: if the structure is high enough, it could be some hooks that catch the net, not horizontal by at 45° vertically, and so take all the force mostly in tension and not compression, more like cables and so very resistant for a very low weight.
As a note, at this point I made an error of calling them "grid fins", they would just be top-legs, automatically doing the same stabilizing job as the grid fin hanks to their length.
Stage structure resistance. The stage is not conceived to support top-legs, but the rocket weights 325t at lift-off, so I suppose 20t on a smoother landing should be OK without too much reinforcement
Movement of the barge that would make the top of the net very unstable. Good point. But the barge is very big (50 $\times$ 90m) so it is quite stable, and we could add very heavy and deep keel (not sure of the word) to stabilize it more, as it doesn't need to move fast at this time (it may already be the case).
The net would break if rocket would come too fast. Absolutely, but the rocket would still slow down to almost 0, like now. It would just have a little more flexibility, could come slightly faster or less straight.