The hardest part of space travel is probably fuel economy which is why it makes little sense to see the booster rocket land on its own power. Sure, you can do it, but if you rely on your rocket engines entirely to decelerate (as the video clearly shows), you would need roughly double the fuel. Instead, what NASA and every other space agency has done, is to rely on parachutes and air resistance (yep, all the fire on the bottom of the shuttle, or a mercury capsule means that air resistance is actually slowing the spacecraft down). This is much more efficient. Another alternative would be to use the boosters for the final few seconds.
And yes, I learned this playing Kerbal Space Program and Elon should know better since he plays too;)