I agree that Carson may have had a chance to get further in the game if they had taken out Miesha over Shanna but let's look at those weeks that were spoken of earlier and see why they lead to where we are now.
Week one Carson takes himself off the block and is replaced with Teddi. Now, lets see, who was Teddi aligned with? Oh that's right, it was Carson, Cynthia, and Shanna yet somehow, even though Carson and Cynthia were loyal to Teddi and voted to keep her, Shanna went into the diary room and voted to evict her. I say with friends, allies, like that...oh, never mind. Let's just say it was indicator #1 that Shanna couldn't be trusted.
On to week two when Kirk was hoh and Shanna won pov. With Miesha and Todrick so dead set to target Carson, if she was so loyal to Carson, wouldn't a good alliance partner at least try to use that pov hoping to get either M or T evicted? Instead Shanna decided to pocket the veto leaving both Miesha and Todrick in the game. She could have at least given it the old college try but she didn't and that's indicator #2.
Week three, Carson is on the block again thanks to Miesha still being there even though they had the perfect chance to get rid of her (you want to talk about lack of brain cells?) and Shanna is starting to realize she'd better finally jump on the Carson/Cynthia bandwagon because she really has nowhere else to go. So this time, with the pov burning a hole in her pocket, she uses it and gets her fellow floater/ally, Kirk, backdoored... and then she doesn't even have the decency to throw him one stinking sympathy vote! I'm sure Carson saw that as a great show of loyalty (he didn't) or, more likely, too little too late and too cold. And, indicator #3.
Carson hasn't gotten where he is in his life by being dense but how hard would it be for anyone to believe that Shanna had been double dealing the entire game especially when, in fact, she had! Personally, I think Carson saw it as three strikes and you're out and we're back to better the devil you know than the one you don't.
You can say Shanna got evicted due to a bunch of lies, whatever they may have been, but I can't see why lying would be necessary when all the facts are there (other than it's a BB rite of passage. Let the backstabbing begin!). The person ultimately responsible for Shanna's fate is Shanna herself not being loyal to the alliance she claimed to be a part of and it started at the very first vote.