In G&K culture was obtained to get policies which lead to a cultural victory. It's not like it did anything else, so why would this new culture system do anything other than lead to a culture victory?
No, getting policies most certainly had an effect on the game. In that each policy helped you. Accumulating tourism has no impact whatsoever on your game, except on the off-chance that a city flips to you. As boring and menial as culture wins were in vanilla and G&K, they at least gave you a bonus every rung of the way as you unlocked new policies. In that way, BNW's culture victory is actually a step backwards.
Let me parce that out a little bit. Yes, it's true that generating tourism is more dynamic than the old culture wins. You have to be proactive, getting/trading works and artifacts, finding sites for landmarks, setting up your theming bonuses, etc. So kudos to the developers for making that more interactive. The problem is that accumulating tourism is just a binary proposition: either you have enough to win, or you don't. Imagine if Domination were like that. You build units, and once you build your 100th unit, you win. There's no dynamic, no interaction, no incremental advantage or intermittent reward. You just wait until you hit a threshold and then you win. That's what tourism wins are like. Your intermittent reward is the leaders bothering you about blue jeans an pop music. With Science and Diplo wins, at least what you're pursuing (techs and economy/alliances, respectively) advances your position. Not so with spamming out tourism.
Given all that, I'd honestly I'd rather have the old culture victory back. I wouldn't have the semi-interesting process of building up my tourism per turn, but at least the victory condition I was working toward would actually have an effect on the game. That effect-black-hole really kills the enjoyability of that victory condition.