The catch looks amazing, but one thing I don't understand is why SpaceX needs the technology to catch a booster they've already demonstrated the ability to land boosters on barges. Is the arm more cost effective to scale compared to a barge?
In short, it would require such huge and heavy landing legs and landing barges that it probably wouldn't be feasible.
The second link seems to show a version of Starship that's relatively up-to-date.
On the other hand, I imagine you could wipe out any benefits to $/mass launched pretty quickly by blowing up the tower.
Also landing on the launch pad means you don’t have to transport the rocket. Just have the arms set it down and you’re ready to launch again.
For Falcon 9 that's not that big a deal because they're NOT trying to reuse the second stage. Whereas with Starship they need more fuel to recover the ship, and that means they need to save weight elsewhere to avoid losing too much payload to orbit.