I think it will raise security issues with phishing. Imagine someone registering .con .orgs or .couk to impersonate a .com .org or .co.uk site.
I think it raises usability issues. .com (and it's ilk) identify a particular string as being a website address. With .anything how do you know if this string even refers to a website?
I think it will create bugs in some programs that assume that URLs have only a certain small set of TLDs.
TLD registration is not free-for-all like domains are. I extremely doubt ICANN will accept those. And before people claim "they will for the $200k", let me put your fears to rest: they already keep the money even if the request is denied.
You have a dev box on your network called 'test1'. You can host a dev environment there and navigate to it at http://test1 . Works great, until somebody registers 'test1' as a gTLD. Then you get namespace conflicts.
<tinfoil-hat gasMark=3>Preferential network treatment for corporate TLD's that are willing to pay would be the obvious starting point for telecoms providers. If they are popular enough you can then place heavy restrictions on standard domains and try and sell the result as a 'safe' internet.</tinfoil-hat>
Not that I think that this would work very well in the long run.
What problems do you see this creating?