IKEA does have online shopping, just not for everything they sell.
Considering that IKEA sells probably fifty times the amount of stuff those other places sell, it’s probably a much greater hassle and expense for them to have an online storefront. And like I said before, it’s not in their interest to create a competitive online presence.
I never thought about it before, but I think this might be part of the key to why IKEA resists the online market. All of IKEA’s packaging would have to be redesigned in order to ship safely. IME, the way that things are packaged would in no way hold up to the abuses of transit. They’d either need an additional packaging step (i.e. put the already packaged item you bought into a larger box with padding, etc.) or redesign the existing packaging in order to make it shippable. That’s got to be a huge cost beyond the issue of just setting up a picking/shipping facility to accommodate mail-order.
I wish Nashville had an IKEA. 
Just for that, I’m going to chime in and say that I love my ikea computer table. It’s got about 2 miles* of real estate for me to spread my work out on, it looks great, in a minimalist sense, and I’ve taken it apart and put it back together about 3 times. My only worry is that the screws will eventually wear out the holes, but if that were the case, I’d shift the desk-top over 2 centimeters and drill a new set of holes. 
I had an odd online experience with IKEA a few years ago. I found a metal daybed frame on their site for about $100 and was able to place an order. At checkout I was informed that I would be contacted with the total shipping charges and could then confirm my order. I’ve bought other assembly-required furniture online with reasonable shipping charges so I didn’t expect a surprise.
But I heard nothing for weeks, so I contacted them with my order number. Their response, finally, was that shipping would be $250! Needless to say I canceled the order. I was left scratching my head. What were they thinking? Why offer the bed online at all? It seemed an odd sort of bait and switch. Cute daybed though.
FWIW, I have two couches, three chairs, a bookcase, and a table from IKEA, all purchased online and all delivered to my door for a negligible shipping cost.