Couldn't you just like find a more efficient fuel/oxidizer mix? Or is this like fundamental chemical energy density? Does it make any difference if you just have to fly in atmosphere, and not escape Earth's gravity? Seems like it should be easier...so you could have more payload.
Precisely. Rockets use liquid oxygen and cryogenic, extremely weight efficient fuels (usually liquid hydrogen or liquid methane). They are pretty much at the edge of practical chemical energy density.
> Does it make any difference if you just have to fly in atmosphere, and not escape Earth's gravity?
But they have to fly for a much longer time, with atmospheric drag. If you look up examples like the Me 163 and the X15, you will see that their range is extremely short:
https://en.wikipedia.org/wiki/Messerschmitt_Me_163_Komet
https://en.wikipedia.org/wiki/North_American_X-15
The reasons rockets use rockets (and not jets) is because their flight time in the atmosphere is even shorter, and they need a ton of thrust in that short period, not because they are particularly efficient.
https://www.marssociety.ca/2021/01/07/rocket-physics-the-roc...
TL;DR Rockets on launchpads have about the same fuel weight/body weight ratio as a soda can, with the soda being the fuel. A rocket airplane would similarly need to be mostly fuel.