The suggestion of gifts reminds me of Dragon Age Origins, and gifts kinda trivialized that approval system to where it might as well not existed.
Though I think we should be allowed to give certain items to companions that are relevant to them, like Wyll's eye. Some gifts and some more quest/story related. But not as an entire system where you gift tons of gifts to raise approval.
I think this system steams from JRPGs, they are very simple in that regard.