Perhaps someone may have a better answer but what I can think of as the reason Chrome does not support many applications yet is because they have to invest in R&D and more importantly the reverse has to occur. I believe that the application developers have to also support Chrome. Adding support for a complex application most often requires heavy investment. If chrome sticks around for a while like it looks to be doing, perhaps it will be more mainstream for developers too. The cost of developing and testing an application has to yield a return, IE is always available but Chrome is an add-on. It is easier and much less costly for an application developer to state they only support IE. If they up-front claim not to support the other browsers, they don;t have to use resources to maintain its compatibility.
Over the years, Internet Explorer has seen more than several challengers to the thrown of being the number 1 used browser. Application developers also know this. The default standard is Internet Explorer. When a developer begins his work, the initial goal is not to make it work in chrome or Firefox or any other browser, it is IE. It is always IE. Netscape many years ago came close to challenging IE for the title of the number one used browser and perhaps owned for a very short amount of time. The other browsers come next for developers if they are considered at all. (Image is from news.cnet. com)