Methane is very low cost (where pipeline networks exist), will probably still be comparatively low cost in the synthetic fuel age, and is much easier to handle than hydrogen. Big airports could have LNG plants on site, smaller ones would have to truck it in.

Methane-based planes might have a lower TCO if the industry made the switch but the switch would be hard.

I don't think you can talk about the engines being the problem if the supposed alternative to kerosene-type fuels are methane and alcohol - the engines are probably the easy part of the problem there; it's the pressurization or cryogenic requirement for methane and the significantly lower (~half?) mass energy density for alcohol fuels.