For many "ordinary" chemicals, the so-called process temperature is the challenge with carbon-free. Not dissimilar from steel or aluminium making (melt the ore first before reducing it).
https://www.c-thru.org/wp-content/uploads/2022/12/Ammonia-Te...
"Generally, in the ammonia synthesis loop there is no need for an external heat source because the ammonia synthesis reaction is exothermic. The produced heat from the reaction is a high-valued source which can be recovered to satisfy the temperature requirements of the converter feed-stream and to generate high pressure steam for use in other plant processes. In modern plants, the compressors of the synthesis loop (the syngas/recycle compressors as well as the ammonia refrigeration compressor) are usually centrifugal ones driven by steam turbines which work with the produced steam from the recovered waste heat available within the plant (European Fertilizer Manufacturers’ Association (EFMA), 2000). Overall, electricity consumption values of ~0.32 to ~0.64 kWh/kg-NH3 have been reported in literature for the synthesis loop, depending on the variations in the syngas production pressure, synthesis loop pressure and compression efficiencies (X. Liu et al., 2020)."
Note that the figure given there is an order of magnitude less than the electrical energy needed to make the necessary hydrogen by electrolysis.