I'm sorry, but this can no longer be used as a strike against Bethesda for bad writing. Eden had a reason. He no longer had faith in Col. Autumn to carry out his will. The Lone Wanderer was a very long shot to be sure, but it was believed he already had the activation code so Eden hoped to appeal to his sensibility rather than torture him for it. Being the supercomputer that he is, he's already calculated every possible outcome, and agreeing with him is the only logical choice.
Yes it can, because no matter how you slice it the entire plot point makes no sense at all. Autumn no longer wanted to obey Eden, that's true enough, but he has hundreds of soldiers and dozens of robots at his command, surely one of them would be a better choice. Or if he 'has' to give the FEV to the wanderer solely for plot reasons, a better explanation than "Oh this will kill every slightly mutated human out there" could have been used by the supercomputer... in other words, he should have had an extremely convincing lie handy.
Here is a lie that I came up with as I'm writing this, right now, off the top of my head: "Hello, Mr. Wanderer. I happen to have a water purification agent handy that will slowly remove all radiation from the Atlantic over the course of the next two decades. Sadly, my men do not know the code to start the purifier, and thus haven't been able to make use of it. Perhaps I should give you the agent along with an armed escort to take to the purifier, and you can put it in for me? You see, we both have the same goals. Let us help one another out."
Would that have worked? Well, maybe not on everyone, but I suspect a LOT of people would have fallen for it. The supercomputer should be smarter than me.
Why in the WORLD did Caesar give me the platinum chip and ask me to destroy Mr. House's equipment in the bunker? Me, the guy that destroyed at least one of his terror squads, clears out every small camp he comes across, and killed the spy at Camp McCarran? He even mentions these deeds. He knows I did them. The radiation was extremely mild, the robots very easy. It required no lockpicking or science skill. If he didn't want to do it himself, he has any number of trustworthy lackeys to send in to get the job done. The only choice worse than me would be a high ranking NCR agent. That is a huge mistake.
You can ask him that very question and he explains it to you. The reason given is that he doesn't want the idea of robots winning their war for them in circulation. He wants his underlings to have the mentality of warriors, and he would have to send someone valuable down there he trusts enough to get the job done, and then kill that person.
To give my own personal thoughts on the matter, if you actually look at Caesar's personality throughout the game it's not at all out of character. Caesar has been in the habit of giving orders and being obeyed without question for so long that disobedience is something he doesn't expect anymore. If you refuse to do as he asks on any mission, or question him at all he throws a tantrum.
Oh, and don't forget he has a brain tumor. So we can compare the brain damaged old man's mistake (that is still suitable for the character), to the obvious blunder of the supercomputer... which makes less sense?