Based on the conversation between Obi-Wan, Mace and Yoda in AOTC.
The conversation in which Obi-Wan expresses concerns for Anakin being ready for this solo assignment? In which Windu points out his skills being "exceptional"? Where Yoda attempts to teach Mace of his own growing arrogance and it flies right over his head?
Nothing they say tells us there are any expectations on Anakin. All Mace says about the prophecy here is that IF it is true, then Anakin is the only one who can restore balance. He's still not convinced, let alone expecting Anakin to save the universe. And even if he did, Anakin isn't in the loop on this, so it's all moot. He can hardly feel pressured by a conversation he's not even present for.
What's more, this mission is meant as a test of Anakin's skill and character, nothing more. And let's be clear; it's a simple babysitting assignment. He's supposed to go to a very friendly, comfortable world, and sit in an isolated secret retreat with a Senator, watch for more assassins, and wait until Obi-Wan has done all the real Jedi work and it's safe for her to return.
And so of course he creeps at her, tries to seduce her, then runs off and murders a village of women and children, and gets his arm cut off because he thought going straight at one of the finest saber masters in the Order was a good idea.
I'm not saying he didn't. I am saying that being treated differently isolated him further with Palpatine ensuring that he was.
Well a secret Sith Lord is always going to be wildcard, not really something that could have accounted for, what with the whole "secret" part, no?