I'd highly recommend the following experience to all players who are having incredible frustration, rage-quitting, or potentially losing interest in the game(heaven forbid) due to the AI wonder-sniping by 1 turn.
Try a game with a powerful, unbalanced civ (Babylon, Poland, Korea, or a properly-situated Aztec.) Turn the difficulty down one notch, re-roll until you find what you consider to be a ridiculously good map setup - maybe even download the IGE just to save some time and tailor the best conceivable (but realistically possible - no 9 luxury capitals) map. Now go through the game without building a single world wonder. Your goal is to create the most runaway, powerful civilization that you can manage; put yourself in a position where you're a god among insects and see just how powerful you can become. When a victory condition becomes available, don't complete it, rather continue on to see just how powerful you can get. Can you reach 700 GPT? 1000 GPT? A treasury of 150K? 500K? Can you complete 4 SP trees and have a well-developed Ideology? A military 10 times stronger than the rest of the world combined? Eradicate everyone else down to just you and one other crippled capital? Then remember that you accomplished all this without building a single world wonder.
I did this when I had trouble moving from Prince to Emperor because I had difficulty accepting what some of the veterans were saying. I understood that engaging in wonder construction was a gamble but couldn't imagine I'd gain enough power without the bonuses. And I especially had difficulty accepting that even if the wonder paid off, it wasn't worth the opportunity cost. After doing so, I found that my expansion occurred significantly earlier, helping the capital a bit but having powerhouse secondary core cities. Military was 3 or 4 times as strong as it was before, now I was dictating who declares war on who, and when. Big bonuses were lost, but more options and better options were available.
Then try to same experiment on your current difficulty level. Not only can you further your understanding that wonders and player score don't indicate power, but also you can take note of when wonders are being completed so you can better assess when they are an option.
Sincere apologies if this comes off as condescending or dismissive, but world wonders in this game are akin to training wheels, and the game becomes much more flexible and consequently engaging when you take 'em off.