This.
Synthesis efficiency is on the order of 60%. Combustion efficiency, driven by Carnot's Law, ~30--50%, possibly a bit higher for combined and/or power-to-thermal. But the overall round-trip efficiency, based on both synthesis and generating losses will be low, 15--25%, perhaps as high as 30%.
The goal of such a system isn't efficient storage so much as it is persistent and dispatchable. It's possible to store large quantities of liquid fuels for long periods of time and tap into them within seconds or minutes as generating, or other fuel-based energy applications, are required. Other storage/release options either don't have the long-term storage capability, or cannot be ramped up as quickly.
Other storage options range from the exceedingly short-lived but responsive (supercapacitors, kinetic flywheels) which can respond on a sub-second to second basis, but aren't viable for long-term storage at all, to options which work over a few hours, daily supply-demand inconsistencies, etc., such as pumped hydro and high-termperature thermal storage (e.g., molten salt), to seasonal thermal storage (hot water, ground geothermal where geology supports this).
Fuel synthesis makes sense where there's exceedingly high seasonality in energy generating capacity (e.g., summer vs. winter for PV / solar), or where there are longer-term highly-variable generating trends (e.g., wind, with higher and lower output over the course of days or weeks). Or where communities are highly isolated and cannot readily be connected to a grid to balance consumption and generation over time (remote islands, arctic communities), or where a region has a very high generating potential but low domestic demand (say, northwest Australia, with sun-drenched deserts and low electrical demand from sheep and roos).
Banking summer-time / high-production capacity as fuel, and drawing down those fuel reserves or shipping them to areas of high demand could be the shape of a future energy economy. It should dramatically rewrite energy geopolitics.