Your anecdote is good to keep in mind, I learned something. While I don't think the US has any auto-cut places (oh the liability!), we certainly have had infomercials selling vacuum haircutting machines for a while[0]. I'm not sure they've made a huge dent in the beauty industry to date.
Beauty is not an industry that a bit of tech pixie dust will magically transform. Haircuts aren't just a utility, they're a personal statement and a piece of one's identity. And as a previous poster indicated, it's also social and cultural. Plus the variety of people's hair and variety of desired cuts make it an incredibly complex and fine motor skill, one that robots will suck at for a very long time. And people rarely know exactly what they want when they go into a hair salon, so there's a service component there too. Beauty just isn't ripe for disruption because people and culture are so involved.
I think this is similar to the soylent discussions. Food-as-utility people think its great, but food has cultural value far beyond calorie intake. So its found its niche among products that already existed (sans tech pixie dust) - the nutritional shake market.
90% is an order of magnitude off in my opinion. But I agree that a place that offers reasonable hair cut for cheap is what many people would want, so I do look forward to your future where that is offered!
[0] http://www.flowbee.com/ http://www.haircut.com/ http://www.aircut.com/