I mean I typically can be friends with at least some of the AI players but my problem is that it usually doesn't feel like it was due to any conscious effort on my part. The AI that starts next to me and crowds me is going to hate me no matter what because I am going to kill that guy and take its land. Probably get knocked out of the game. Then the other Civs will either hate me or not after that. I have very little impact on that. I've tried giving them free resources, but the positive diplomatic modifier doesn't seem to make a meaningful difference to their opinion of me. I always send delegations/embassies the turn I meet a new Civ to get that going (but if I don't have it later sometimes they will or will not accept them seemingly at random). And some people are going to hate me because their agendas cause them to hate people who play the game well. Other people will like me because their agendas cause them to like people who play the game well. Either way, I'm not going to stifle my empire just so an AI player will be my friend, since I gain so little out of it and there's also little price to pay for them all hating me.
It's not that I can't be friends with them. It's just that (a) there's not enough reason to be and (b) it doesn't really feel like my actions have much of an impact on their opinion of me.
I hate to say Civ IV did it better because it's almost a mantra at this point, but really, I did like how Civ IV did it: if you have X positive diplo modifiers, they are pleased. This means they will make certain deals with you and the "Pleased" indicator is clearly there for you to see. Certain leaders will consider attacking you at this point, but most will not. If you have Y positive diplo modifiers, they are friendly. Again, "Friendly" is clearly displayed, they won't backstab you (except for very few leaders, I remember Catherine would), and they'll accept more deals. If you don't have very high diplo modifiers either way they are neutral. Etc. Numbers very clearly translated to relationship states, and those relationship states told you what you could do. VI is very different. I can have all positive modifiers and be "unfriendly", because there's some behind-the-hood workings going on. There's speculation on that, but nothing confirmed. And even if I do get the "Friendly" popup with a Civ, that doesn't mean they'll sign a Declaration of Friendship (you know, like you might expect). What does "Friendly" even mean in that case? Sometimes, they'll sign a DoF. Sometimes they won't. I don't know. About the only thing that seems consistent is if you dip very low in relations they will hate you forever (usually due to warmongering). If numbers very clearly translated into relationships which very clearly translated into applicable diplomatic interactions, then it'd be better.
Plus, in Civ IV, they would tell you why they were refusing a deal. Also very helpful. "We have enough on our hands right now"--they're going to war with someone (possibly you, better watch out) or already at war. "We just don't like you enough"--not enough modifiers. "We would have nothing to gain"--either already have that resource or they're refusing war because they don't feel like they can capture and hold territory. "We couldn't betray our close friends"--they're not going to backstab someone they like. Etc. etc.. Seriously, this transparency is a good thing for a strategy game, because it lets you plan and react to changing situations. But you know why they're changing, and that's important!