Many benefits but it all boils down to preference. Having the target dissolved in the liquid phase allows for the liquid phase to be reduced in volume via heat to do pulls from easily. For example an STB often requires turkey basters and big jugs when scaled up to say 200grams of plant material. An A/B with a similar amount of biomass can have it's pulls done in a 250mL separatory funnel without a drop of sweat.
There is also less volume to dispose of later, and it requires significantly less sodium hydroxide or similar base.
Unless you mean in general, aqueous verses a dry extraction? Again less base needed, and no need to evaporate or boil off water from an alkaline solution to make it 'dry'. Probably a lot easier to mix a liquid bi-layer then a solid/slop and a solvent. It's all preference.
Wet chemistry is pretty important in general, I assumed you were referring strictly to extractions.