that surface area exposed is in relation to the *RATE* of saturation; saturation will go to completion and in accordance of thermal 'swings' that lag the actual ambient temperatures. Otherwise your argument 'doesnt hold water' .
Diffusion to saturation is governed by *rate* of chemical equilibrium.
Mass transfer simply isnt dependent on surface areas rather chiefly due to equilibrium states .... if it was you couldnt explain the ultimate water saturation of dielectric oils through essentially hermetically sealed metal containers (transformers and tap changers) in the power generation industry, etc.
Using your 'premise' the world wouldnt need water wells, all that we'd need would be to place out empty tanks and expect them to magically fill with water .... and that does not happen.

I too am a physical chemist plus an engineer in fluid/thermal sciences with well over 40 years experience in molecular separations/dehydration within ultra-pure chemistry and advanced engineering experience working directly with such 'saturation' processes, etc. ... chiefly as a 'particle guy'.

*Condensation* on such internal tank walls ONLY will occur AFTER the tank fluid is nearly saturated with water, not before. Literarily speaking condensation is a symptom that the oil is now 'wetted' with water and has or is nearing equilibrium with the water content of the atmosphere to which it is in connect. No oil in the tank = no to very little 'condensation' and if minuscule water does condense will rapidly equilibrate back to the atmosphere during changing thermal differences ... system is in equilibrium.

Rx: No to damn little oil in the tank = no water at the bottom of the tank. No water then no need for bacteriostats and anti-fungals, etc.