> Bind searches to domain names, eg "food in chicago" => f02970848a63988965aa40cd368ffcf9046209ca.com
This IMO is bad, and goes in completely wrong direction. We've invented search engines to have such phrases not bound to a particular domain. Who would handle the "#://food in chicago" domain? Would it be Google? Bing? Yelp? Local restaurant chain? Or maybe some scammers? And who would maintain the completely different website "#://food in Chicago", and why "#://Food in Chicago" wants to silently install me some malware?
The reason searching for such phrases makes sense, while having them as domains does not, is that things like "food in chicago" are poorly defined, fuzzy concepts. It would feel weird to change one letter in a query, or replace word "food" with, eg. "something to eat", and see completely different website. Moreover, major search engines are more or less egalitarian wrt. buisnesses. Yes, there's the whole SEO thing, but you can't get full control of what food joints are listed near your location just because you've managed to get the register first. I can (and do) trust listings from Google; they have both incentives and track record of being fair. I will never trust listings from random-autogenerated-squat-scam-business-site.
Which brings me to the second point,
> Good domain names are pretty scarce. It's a source of frustration for anyone who has ever tried to buy a domain.
Yes, they are, and the primary source of frustration is that they are mostly taken by various squatters and other scums of the Internet. What will happen is that, the moment there's any real possibility such hash-domain scheme is introduced, all those evil people and companies will take all the domains like "#://microsoft", "#://android" and "#://insert any popular keyword or phrase here" in order to sell them back to real businesses for boatloads of money. And then we'll be back to square one, with maybe a little bigger domain space than we have right now. Bad people win, good people loose and nothing changed.
So, again, the concepts behind this idea elude me.