I decided to play Beyond the Sword with some relaxed settings: Single player > Custom Game > No Barbarians, Always Peace. This is the second game in a row I'm playing with these settings, and the previous one went smoothly - as expected, I had a cultural victory.

Well, this time I reached three cities with legendary culture.... and nothing, So then I decided to go for a diplomatic victory, and started bribing the AI players. And I got more than enough votes at the UN..... and nothing. That's when I realized that something is b0Rk3d.

Does any of you have any idea WThell is going on?

I started another game, and again achieved legendary status in three cities (I am playing at normal speed, so legendary is at 50.000 culture points). See attached screenshot.

EDIT: turns out, even though I play at normal speed, the culture points needed for legendary culture of a city are 100.000?! Very strange.

This is because you have turned off espionage. Then espionage points are converted to culture, hence the need for 100,000 points instead of 50,000. It's a pretty big downside though, because you also need twice as much culture for everything else, like expanding borders, which is a big pain in the early game if you are not a Cultural civilisation. Instead of 10 turns with a monument or a religion, you need 20. Plus, it's harder to scale up espionage points than culture points. For starters, culture buildings double their output when they have been in existance for 1000 years. Which is why it's important to build important wonders and such asap, or let's say before 500BC. Way later in the game, and those 1000 years tick by much slower.

the problem is you are playing easy settings and not challenging yourself.