Uh sorry people. But what your telling about the AI bonuses is just not true.
The AI does
not get unlimited or free money. The AI does
not get free research and production points. The AIs stuff does
not get everything multiplied by 200 so they would have 1200pp factories. Thats just bullocks. (Sorry for my language).
What the AI gets on higher difficulties are certain boni. Think of them as the same as the ability boni you can pick at the beginning of the game. The 200% economic bonus for example doesn't mean that they have 200times your money, thats just +200% or three times your amount. Those stellar numbers you're talking about would make the AI able to research the whole technology tree in about 20 turns...
Reason people. Reason! (Think of Homer Simpson yelling that.

)
No seriously. The boni the AI gets aren't that high as you think.
I'll explain this with a game example.
Drengins:
44pp x (20% + 300%) x 0.3 = 42.24 (41)
44pp x (40% + 300%) x 0.27 = 40.392 (41)
32rp x (41% + 300%) x 0.43 = 46.9216 (47)
First colum is how many social, military and research production was the planet able to produce. Second colum, inside the () is their normal bonus plus the 200% bonus because of suicidal difficulty (it's 300% because I'm multiplying). The third colum is how his spending sliders are set and the second last colum is how much is the resulting social, military and research production which is the same the game screen shows (which is the last colum inside the brackets).
I had to guess the spending sliders of course but as you can see they add to 1 (=0.43+0.27+0.3).
----------
So this can't be the reason, as we can see now clearly.
Imho the overuse of embassies is because the AI wants to fight against Influence which is threatening him. But since those embassies are so weak (25% is nothing) they have to build too much of them to be any use. Personally I would like to see them just to build some influence bases. Much better and cost effective.