I suspect the simple solution to that is to have low cost models in a range of sizes try on each item. Let's say it costs 100$ a per size * 10 sizes = 100$ per item in your catalog * 10,000 items in the catalog = 10 million. Which is within the range of a well funded start-up. So it adds 1k/item and some lead time it's also a huge barrier to entry and probably well worth it.
PS: Don't forget Zappos sells shoes online where fit is both harder to come by and more important.
If I'm in the target market for high fashion, I'd probably list "clothes shopping" as one of my hobbies. I don't; I buy cheap clothes which retailers make minimal profit on. If I was in the market for designer clothes then my tastes wouldn't be price elastic, so saving retailers' costs by substituting cheaply made model videos for the user experience of actually seeing and touching the clothes in a stylish location isn't much of a purchase incentive. By contrast, unless the local Blockbuster outfit offer exceptional advice, actually going and physically picking up DVDs is a mere inconvenience and I'd much rather pay less to skip it altogether.
I'm not arguing it's impossible to sell fashion items online; it evidently is. It's probably also possible to sell wallpaper over the telephone. That doesn't mean the economies of selling over the internet necessarily lend themselves well to disrupting a sector that enjoys massive profit margins through making far more effective emotional inducements to purchase than a photograph and a like button.
I would argue that there is a huge market for people living in Arizona that can't get to any of those high end stores without flying there that still buy 'high end' fashion. The market is fit 34 year old doctors making 300k that don't live near such stores it's really poorly catered to. When a catalog sell 5,000$ dresses based on pictures that look nothing like the customer that's just ripe for disruption over the web.
You could also do the same thing for the mass market, but I don't think the average American really wants to see someone that actually looks like them trying on the clothes. Granted, there are main stream markets other than fat that this could work just fine, baby clothes, teens, big and tall etc.
Yep - there is a huge market for this, one that Net-A-Porter and Mr. Porter dominate (~$200 million in revenue). They take care of the sizing issues with flexible returns and personal stylists. Since 80% of their revenue comes from only 2% of their client base, they can afford to hire personal stylists for higher-volume clientele. Check it out.
PS: Don't forget Zappos sells shoes online where fit is both harder to come by and more important.