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Once they have achieved sub-meter precision landing, getting rid of embedded legs in favor of external “legs” only makes sense.
Does it? Genuinely asking. I would expect the precision involved to do this to be a lot higher than when you have actual landing legs, which would provide some bit of “buffer” for hitting the target landing point. A RUD that takes out the first stage is one thing, but a RUD that takes out the first stage and the tower?
a) I think for the landing they will use a different tower from the launch tower. Launch tower has fuel/oxygen lines and in general is not well suited for landing catching role.

b) I would imagine landing tower(s) as lightweght specialized structure that can move relatively fast to catch a rocket within +/- couple meters of ideal landing center.

That's an interesting idea. A landing tower, built to refurb the first stage before wheeling it back over to the launch tower for refueling and then another launch.
It's my understanding that the purpose of landing at the launch tower like this is to reduce refurbishment time rather than to lower weight from the legs - their stated goal is being able to re-launch in under an hour after landing. Having a second landing lower would add similar delay to simply landing at a pad.
I wondered when they would finally ditch the landing legs. It’s just an extra added dead weight.

One technique is to reinforce the rocket base with more metal padding, and then on landing, the ground-based robotic clamps would magnetically lock on to the reinforced metal padding.

Or they can do it this way, and have a magnetic picker lock onto the top of the rocket. Then it would gently lower it to its final resting position.

But I think they would have to hover the rocket for a few extra seconds, while the robotic arm moves itself into place to perform the final catch. This would require more fuel, which reduces payload capability.

Awesome. That's similar in concept to Zipline's recovery system. The vehicles have a tiny tail hook, and a motorized ground based system snaps them out of the sky. The engineers that work on that sort of thing must be really smart, cool people!
Great example of designing things out and ‘why not just?’
As crazy as this sounds, it requires a hell lot more precision at this point.

But perhaps their engineers have already designed and tested different aspects of such a system.

Wondering if the catching can be done by making it float down in to a cooling tower size chimney, avoiding the variations caused due to wind.

Elon Musk's tweet: "We’re going to try to catch the Super Heavy Booster with the launch tower arm, using the grid fins to take the load"

That'll be fun. Grid fins tend to be jagged in order to avoid troubles at transonic speeds. That means little sharp points need to be caught on something. Both the fins and the catcher will face enormous stress.

My suggestion: ask a tire company to make sausage-shaped pads from thick tire material with lots of tough fiber. It should resist puncture and be able to withstand high air pressure.