In India we provide such lockout only for OFAF cooled GSUs (with oil to air heat exchangers, having no ONAN rating). Our logic for the same:
1) These coolers will come in to action along with master breaker and not controlled by temperature indicators.So switch of the coolers also with the main breaker to save energy.
2) When a major internal fault occurs inside transformer a lot of carbon slime is generated and spread through oil. So a good practice on such occasion is to drain out oil as soon as possible so that carbon will not go and settle on winding paper insulation. Once settled, it is impossible to remove the carbon from paper. So stopping of pump is essential especially with directed oil cooled units, to avoid carbon moving in to winding.
I do not think running fans will any way fan the incipient transformer fire. It is too feeble to affect the oil fire. The fans usually will be sucking air and pushing it away from the transformer. Most of the fires start from failed HV bushing, well away from the coolers.The oil fire intensity is too strong to be affected by air flow from fans.
Many years back, Tokyo Electric Company never allowed the use of oil to air heat exchangers with aluminum tubes and insisted for steel tubes. Their argument: in the event of a fire aluminum will melt early and the oil coming out will feed in to fire !