I posted about my dairy-free short experience here, and suggest you read the thread mainly for the comments of many other people who tried dairy-free for various reasons
http://forum.lowcarber.org/showthread.php?t=457032
The main thing that pushed me to try dairy-free (well, dairy-light, I did keep butter in my diet) was one sentence in the Jenny Ruhl Diet 101 book - "I've even seen people suggesting that it was the 7 grams of "hidden carbs" in a cup of cream that stalled their diet, rather than the 820 calories that cream contributed. Overly carb-centric thinking leads low carb dieters to come up with some very questionable explanations as to why high calorie foods stall them."
There is no question that for me I need to keep a lid on both calories AND carbs to lose at a pace that I consider to be motivating (I also try to keep protein moderate at around 65g per day). I'm in my 40s and don't exercise much, so this is a personal thing and probably is different for each of us, but from what I've seen middle-aged women very often need to keep calories in check as well as carbs.
So eliminating dairy for those 3 weeks cut out a big source of calories. And I think that's why Atkins limits cheese and cream in induction (along with some who theorize that dairy spikes insulin in a different way, and that might be part of the rationale of limitation).
I should say I don't have any problems with sinuses, skin, etc - the things many people say improve when they remove dairy. I've also never had intolerances to lactose when I drank milk, so I think I'm maybe one of the lucky ones who tolerates dairy well.
Since my little dairy experiment, I had a few weeks around the holidays where I went back to cheese especially (I only bought cream once though - when I caught myself drinking extra coffee and taking two spoonfuls in one day I realized I was MUCH better off without it in the house). After the holidays I've had small amounts of dairy but infrequently - an ounce of cheese on my eggs once or twice a week (but never for snacking), a quiche made once a week or less (cream, cheese), and I usually make a pot of veggie cream soup once a week that uses about 4 oz cream cheese for the whole thing (about 6 servings). All in all, I think I'm now "dairy-light," consuming at most a quarter of the dairy I took in before my little experiment.
And I should also add that my weight seems to be stalled right now and among the things I'm considering (other than PATIENCE - my primary strategy!) is to return to cutting out dairy again.
Good luck as you figure out what is right for yourself!