An operating system is like a table.
A browser or other application is like an item on top of the table.
Internet Explorer is an application, but it's PHYSICALLY part of the table because of how Microsoft bundled it with the OS.
Even if you don't use IE you really need to install updates. If a hacker gains entry to your system, they may attempt to abuse a known vulnerability that you could have patched but didn't and then your problem is compounded. Additionally, since IE is a shell used by some other browsers (and other applications), if you're using one of those tertiary browsers (such as Maxathon) you would be stuck with an older version of IE that renders the pages (even though the interface is something else).
When dealing with vulnerabilities, you need to do a cost/benefit analysis; does the cost of the downtime to install, and any compatibility problems it produces, outweigh the risk or loss incurred from an attack?