I was watching this video from Everyday Astronaut:
In the video, it highlights why Stage 2 landing is considerably more difficult than stage 1 landing. There is a 1:1 payload penalty in stage 2 as compared with 5:1 in stage 1. Also, stage 2 travels at 8km/sec vs 2.5km/sec in the first stage.
Another big problem (as per the video) is to keep heat shield pointing down during stage 2's return. Since the heavier engines tend to gravitate down towards lower CG while the empty fuel containers tend to point up.
The current designs attempt at using boosters to keep the shield facing down. But since the object is in an unstable equilibrium, any deviations are amplified, making the design an excruciating challenge.
Why don't we use a hollow cylinder design? By keeping the engine pointing down and a ventilator shaft at the top of the rocket to bypass the hot air from the atmospheric friction. Engine is already build using extremely heat resistant alloys. It should be able to withstand the friction heat, which is now lowered due to bypass shaft. The sensitive areas inside the engine can be shielded.
Hollow cylinder design will not help much to reduce the craft's speed during atmospheric re-entry. But it can reduce the heat problem, which is about 64 times stage 1. We will have to reduce the rocket's speed considerably after a successful re-entry though.
All the numbers and assumption are taken from the above video. Please point out if these numbers are wrong.
+1for a genuine question asked in good faith based on information from a video made by an "everyday space expert!" ;-) $\endgroup$