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What is says on the tin.
Whatever the reason, be it poor metallurgy, or no Whittle, or nobody willing to spend the money developing them, what would replace gas turbines as aircraft engines if they didn't exist?
I see two obvious options: pulsejets & ramjets. Pulsejets are fuel-thirsty, noisy, & inefficient. (I also wonder if they're thrust-limited, but IDK enough about what limits the thrust: bore size or pulse rate.) Ramjets obviously can't work from a standing start. So, so JATO bottles become standard (even mandatory)?
Liquid-fuel rockets strike me as too hazardous, fuel-thristy, & complex.