> If the first stage were to "fly" all the way back to land after separating from the second stage
You write it as a hypothetical, but that's actually how SpaceX landed their first first booster. It was Falcon 9 Flight 20, which deployed 11 Orbcomm satellites.
Interestingly, NASA also considered that as a potential abort mode for the Shuttle ("RTLS" - return to launch site). Minus the vertical landing of course. It was the first option that would be available in the event of a failure, immediately after SRB separation. The vehicle would execute a Powered Pitch-Around maneuver and then jettison the external tank, timing things so that they would run out of fuel and the vehicle would have its proper CG for gliding.
The astronauts considered it extremely risky to say the least. NASA actually wanted to try it on STS-1 (a manned flight on a system that had never been tested before) to see if it worked. In the words of the mission commander: "Let’s not practice Russian roulette, because you may have a loaded gun there." Which carries a lot of weight from a man who was willing to risk a lunar landing.
You write it as a hypothetical, but that's actually how SpaceX landed their first first booster. It was Falcon 9 Flight 20, which deployed 11 Orbcomm satellites.
Infographic of the trajectory: https://i.imgur.com/D9BdO86.png