Factors of 2 or 3 in specific power and efficiency are possible. Due to the rocket equation, this could yield vastly longer range and more efficient aircraft (1/10 the weight, 10x the range, 10x the efficiency, 2x the speed...).
In particular, you point out the limitations of the Brayton cycle and material limitations. However, there are other cycles that are much closer to Carnot efficiency, or match it in the ideal case. There's a lot you can do when isothermal compression is possible. Additionally, if there is a thermal limitation, you can do isothermal combustion, such that much more heat addition is at the maximum temperature of your materials, and you can even design efficient reheating.
It's not a jet -- you want to pair this with a driven fan system or at least have high bypass, but it's fundamentally more thermodynamically efficient.
For supersonic applications, scramjets remain possible, but challenging. And rocketry + high altitude flight remains extremely exciting and potentially more efficient than standard jetliner transport. Just difficult.
So yes, there are physical limitations. But they are not what most people think they are, and they do not mean what people think they mean.