Generally I agree with the theme of your question, that in Civ 6 and in life, trade works best when it's win-win. Both sides get something they need/want, and not at an onerous price. In part, this can be affected by how desperate one side is to get something the other side has, obviously. Supply and demand.
Getting the best deal by shopping a spare luxury to multiple AI civs and haggling over price down to the last GP may waste a lot of real time with only limited impact in many situations--not that this hurts you in Civ 6--it just hits up against the constraints of how much time you have to devote to playing. I usually don't spend a lot of time on this because I haven't found it to make a big difference in gameplay, but maybe I'm missing something. I might press for the biggest advantage if I have the upper hand in war and they're suing for peace, especially if they started it.
I did it more in Civ5, I think, such as when I had a Gold resource, or a strategic resource in demand, to trade. Then shopping for the best deal could pay off.
Letting an AI civ "get the better of you" in trade--accepting their offer or even backing it down a notch (le.g. less gold from them per turn)--does help them like you better in certain situations. This is usually only worth doing if there's a particular reason you want that civ to like you better.
If you're playing Domination or they really hate you at say -200 (which can be seen by clicking Our Relationship on the other Civ's screen), letting them win a trade or two will not have any practical impact. But if Our Relationship is neutral or only slightly negative, doing this two or three times can flip the relationship up a level. Give them a gift, or give them two luxuries plus a small amount of gold to their one luxury, if you can afford the hit. Rinse and repeat every few turns, and of course, don't do anything else you know from their agenda that will tick them off.
