If the CPU only has 32-bit ALUs (afaik all CPUs today have 32+ bit ALUs) there is no reason to "support" half-floats (other than converting floats to half-floats for the GPU which doesn't need to be fast or pretty since you do it beforehand and send it directly to the GPU from the model file format).
On the GPU on the other hand 16-bit floats are becoming the standard (the M1 GPU for instance has more 16-bit ALUs than 32-bit). With enough precision for possible resolutions/worlds and you save 2x the memory which makes it a no-brainer really.
If your CPU has vector/SIMD instructions then you might want fp16 format support for data processing so that you can operate on (say) a 128-bit vector of 8 fp16 values at once, rather than having to work with 4 fp32 values at a time. But I agree that there's a lot you can do with just load/store/conversion support.
On the GPU on the other hand 16-bit floats are becoming the standard (the M1 GPU for instance has more 16-bit ALUs than 32-bit). With enough precision for possible resolutions/worlds and you save 2x the memory which makes it a no-brainer really.