Sorry for cutting this post in so many differnt pieces, I just found that there are many different topics that should be approached separately.
I don't know, I win most of my games on immortal. Have not played deity much, so I can't speak to that level.
Well, I win most of my games on deity. 8) And I'm still SO far away from being as good as some of the guys who manage to get some insanely fast victories. So winning the game and having a "flawless" victory are really two different things - by being somewhat experienced in following the popular strategies anyone can beat deity.
But on immortal there is a real risk of being dogpiled by multiple AI DoW's, and with happiness coming from AI trades you can find yourself at -20 happy with rebels appearing in your capitol your economy crashed, trade routes all pillaged, and a massive number of enemy units pouring into your borders while you have a -20 combat modifier. It can quickly end your game.
That's actually rather a sign of you not using diplomacy correctly - which luxury trades are a part of... but also buying DoWs, etc. -with very few (predictable) exceptions you should always be able to avoid wars after the Renaissance by just keeping the AIs busy with each other and becoming buddies with them. That said, generally buying stuff and "buying 20 happiness from that backstab-warmonger neighbor who's going to turn against you" are two different things. You do of course need to be somewhat reasonable at buying that stuff, but that's a skill to learn - and not something that you should avoid entirely.
I find it much better to focus on developing my cities, grow by acquiring policies, technologies, buildings. As long as you maintain positive happiness your cities will grow and if you are only positive because of AI trades you are skating on a knife edge.
Just to make that clear: I'm speaking of BNW here. In Vanilla... sure. Very high risk. In G+K ... weeeeell. Predictable. In BNW? Nope. That's not really a risk anymore as long as you know what you're doing.
The real question is whether it is better to put cash into buildings and border expansions, versus amass excess happiness towards a golden age. If you can time the golden age with winning the world fair I can see the point but otherwise I would rather have aggressive city building.
What does border expansion give you? Your growth is still limited by the amount of happiness. What do buildings give you? The amout of growth is still limited by the amount of happiness. Growth is the factor that influences science the most. And science is the most important thing in the game.
And there is ALWAYS stuff to cash buy. If my capitol had no more buildings left to build certainty my second it third city will. I often do things like save gold to cash buy public schools and universities in my top science city the same turn I get the tech, and then for awhile I am forced to hard build archeologists during which time I cash buy buildings. Ditto while I am building a wonder.
Buying universities, schools and laboratories is something that you can do even if you buy luxuries. Buying most of the other stuff is just a waste - buying stuff with gold is nice because you can do it in any city, even if it's underdeveloped... but it's also very ineffective and wasteful. Think of it that way: If you had spent a part of that gold in getting more happiness to grow further, then you'd not even NEED to buy stuff because your cities would just be more productive and able to build stuff faster. And you'd get science from them. Science! Cashbuying infrastructure that's not a science building (or in some cases a factory) is something that you'd usually do if you play wide, but it should in generally not be needed if you play tall.
@golden ages: If you think you need one to win a world project (again: Bigger cities = more production = you might not even need to), then holding back an great artist to do that job is just fine. Golden ages get more costly the more you had, so it's actually quite useful to NOT get them early and instead get 1-2 more later on when your empire is in full-productive mode.
For these reasons I prefer getting cash from the AI vs luxuries and cash buying happy and culture buildings to get real long term rather then temporary happiness.
Again, everyone gets these buildings and policies. You're just missing out on happiness that "everyone else" gets. Learning how to do this "Properly" - including all the diplomacy that goes with it - might even be what catapults you on deity-level.