> I'm not sure how critical "catching" the booster is to reusability

Not necessarily for reusability, but it helps significantly for rapid reusability: it eliminates the need to transport the booster from the landing site to the launch site. Given that it's 9m x 70m and weighs 270 tonnes, that's not an easy process.

I think saving weight is definitely one of the main issues, see those proportionally large legs on Falcon-9, I guess it simply doesn't scale on bigger vehicles like Starship / Heavy booster. Also, by catching the booster on site, they can even save the transportation and do the refurbishing on site, so even shorter turnaround time I guess.

Also, saving on damage to the landing pad.

That’s a good point, they used the sprinklers on landing to mitigate damage to the pad and the booster was caught well off the ground.

Another way to save weight would be to make the booster out of carbon fiber instead of steel. I wonder whether they will do that eventually.

Efficiency and cost are the goals, reusability is just one way to do that. Moving big heavy things less is another.

> but it does save weight by not needing legs for landing

That was the exact reason they went this way.