The lubrication requirements for engines and transmissions are quite different.
Yes, both need protection from metal-on-metal abrasion, but that is about where the similarities end.
Engines run hotter and have to deal with various combustion chemicals that find their way into the oil. Transmissions do not need to deal with combustion products, but they need certain friction characteristics to support the basic plate-on-plate system.
Multigrade oils can be a special problem if they are not listed as acceptable. For example, 15W-40 is a 15 weight oil that has special ingredients to thicken the oil when the temperature rises. In an engine this works correctly. In a transmission the oil never gets very hot and the viscosity remains low. Full synthetics work in a similar manner.
Of course the transmission can be engineered to use almost anything. However, any given transmission model was already engineered and tested in a specific manner.
The recommendations from the manufacturer should be followed.