Catch Hardpoints
the chopsticks' pins
Here is the strangest idea of all: the booster does not land on legs. It flies back to the tower it launched from, and two enormous metal arms — everyone calls them chopsticks — reach out and catch it in mid-air by two little pins on its side. No legs means less weight, and the booster is already back where it needs to be for the next flight.
How it works
No legs means less weight to carry all the way to space and back, and the booster ends its flight already sitting where the next one will launch from.
For the grown-up
The launch tower carries a pair of electrically actuated arms (nicknamed Mechazilla) that close on load-bearing hardpoints at the booster interstage. Removing landing legs and their structure saves mass and, more importantly, collapses the turnaround: the booster ends the flight already mated to the launch mount.
SpaceX Starship