Stage separation is somewhere around 100km and Mach 6 or more. The exact figures will depend on the mission profile. There's a "boostback burn" at altitude to

Stage separation is somewhere around 100km and Mach 6 or more. The exact figures will depend on the mission profile. There's a "boostback burn" at altitude to slow the horizontal velocity right after separation, an entry burn to put it into the atmosphere, and a landing burn just before it hits the deck. The guidance in between those last two burns is aerodynamic from the grid fins. The first stage mass is ~18,000kg empty (which it nearly is on landing), and it's coming in at its terminal velocity, which is, as a WAG, maybe 70m/s. What's more, it cannot hover, as even one engine has a greater thrust at minimum throttle than the rocket weighs. So it must do what SpaceX calls a "hover-slam", and reduce its velocity vectors to 0 at the same moment its altitude gets to 0 in a single burn. Burn too short, you crash, burn too long, you go back up (and then crash.) And the horizontal vectors also need to be very small, and you can't end up too tilted either, or you fall over. And explode, because you're a thin-shelled tube with plenty of fuel and oxidizer still left. Oh, and you have to hit a very small target within a couple meters. So it's a pretty tricky task. Plenty of rockets can hover these days, but landing a full-sized launch stage coming in from the edge of space is pretty tricky. And they almost got it. Looks like it overreacted just a hair to a gust of wind or something. Your solution has two problems: (1) it cannot hover and (2) you'd have to design and build and test big robot arms. And put them everywhere you want to land. It's probably easier to make your big robot spacecraft, which you already have, do the landing itself on a plain concrete pad.