Can I get a mobile view for every web page on the Internet? Is there an app that lets you view a tiny-screen-optimized version of any web page, whether or not it was coded with this in mind?

Opera's "Mobile View" is like this, but it doesn't give satisfactory results on many pages.  Arc90's "Readability" bookmarklet is also in the similar vein.
Simply put, no.  Web pages are complex to the point where it is effectively impossible to determine what bits are necessary for the page to be usable, readable, maintain the right order, etc. for an arbitrary page.  When you couple this with poorly-coded websites containing errors and the like it becomes quite a mess.  This is why the two things you mention aren't perfect.