I've never understood this need to have a file browser on iOS. Are we still in 1980 or something? Apple has created a more advanced system that works much better IMO. There are a few hiccups that need to be work out though like for example there is no Textedit app on iOS yet. But having the apps directly connected to the files they make is just so much more intuitive than the archaic file management system we've been using for decades.
Your example of browsing for a file and then "Open In" an application certainly isn't faster or more intuitive. That's just what you are used to. It is undeniably faster to open the application first and then open the file you want. Simply because the number of files you have to browse through to find the one you want are narrowed down significantly compared the old archaic method.
I spent 20 years in the MS-DOS - Windows world. I don't know how to use my OS X without a file system.