> need carbon collection on all combustion engine

why not simply centralize the carbon collection and synthesis in some area (preferably where the sun shines a lot), then pipe/transport the resulting hydrocarbon fuel to where it is needed?

Because centralized carbon collection isn't simple. About 0.0427% of the atmosphere is CO2, getting rid of the other 99.9573% you don't want to capture is rather tricky*. The most efficient way is probably by using plants - but that doesn't really scale.

On the other hand, the output of a methane-powered fuel cell is 33% CO2 and 66% H2O - with the water being rather trivial to filter out. Even a dirty regular combustion engine outputs about 14% CO2.