Internet Explorer is a separate process from Explorer.exe. When IE crashes, Explorer does not crash, and I don't know where people get that from. However, if you do navigate to a website within an explorer.exe process (using address bar in Windows Explorer), the whole task bar and desktop will crash if 'start in separate process' in Folder Options is not selected. Just use start in separate process in Folder Options and you can terminate folders as well. This is not the same as 'open in separate window'.
There are ways to remove Internet Explorer from the system without screwing everything else up. Your system will have no problems if you delete c:\program files\internet explorer and all the shortcuts to IE. No problems at all. Many people confuse Internet Explorer with the Shell. IE isn't inseparably close to Windows, however the Shell is. The Shell is comprised of libraries such as shdocvw.dll (Shell document viewer, which also renders web pages for IE), and shdoclc.dll (contains some error pages).
I would not even consider the page-rendering DLLs part of Internet Explorer at all. Those are part of the Shell, because almost every aspect of Windows Explorer and the Desktop uses these DLLs. IE happens to use them too.
You can even start Internet Explorer without iexplore.exe or the whole Internet Explorer directory with a COM object called InternetExplorer.Application. All iexplore.exe does is invoke this object. IE contains a connection wizard and a wrapper to the InternetExplorer object. While this component is in the Shell DLLs, AFAIK it is not needed. WebBrowser is a more general purpose page-rendering control, which the Desktop/Active Desktop uses.
Because the Shell is well-tied into Windows is not the reason it has a lot of holes. It is the reason why Windows shares a lot of holes the Shell object does however.
Most of the IE exploits comprise of buffer overflows in tags, security zone holes (or more appropriately, work-arounds), and ActiveX handling. There are really not that many bugs in IE. Most of this stuff was intended to be so. ActiveX is there so that people can interact with web pages. Unfortunately, many people take advantage of ActiveX with a little bit of social engineering. However this does not mean it's a bug. A bug is something like a buffer overflow, of which IE has a little bit of, but I would not say that is the majority of IE's exploits.
If you want a secure browser, use Opera. It has less total exploits than Firefox (according to Secunia), and zero unpatched vs. Firefox which has at least a couple.