Adofl Lundgren: Yes, getting an FP in another civilization's capital city is good, but it requires you to actually have another civilization's capital to build it in. I often don't have another civilization's capital until the late middle ages or later.
On Emperor and Deity, it is difficult to capture another civilization's capital early on, unless you go for a highly warmongering strategy. What's more, to actually build the Forbidden Palace there, you likely have to use a Great Leader, which is based on an assumption that you'll actually get one, which means you either have to fight lots of wars, or just be lucky. Even if you do get an early Great Leader, he might be better spent on one of the two early important wonders (Pyramids or Great Library) rather than on the Forbidden Palace.
Furthermore, your second core will still require substantial development to recover from the war before it's up to the power of your initial core.
Generally, unless I am incredibly aggressive, and lucky with a Great Leader, I have found that a second core doesn't usually come online until the game is already won or lost.
I generally prefer just to extend my core into a bigger core.
-Sirp.