---while not wanting to radically question #2, it's important to note the E. locution that's very close to the G.

And it's arguably not just a question of register. Certainly in many contexts the verb "to express" will be sufficient. On the other hand, the locution "to give expression to [e.g., your feelings]" introduces concepts that set (or can set) a focus more (in both the speaker's and hearer's mind) not simply on the fact but on the means of expression.