I believe IE was integrated directly into windows in Windows XP; opening Explorer (not internet explorer) was basically opening IE in a view that could browse the OS. Each folder had an associated html file of sorts that could be modified to create custom views and stuff like that (this was Active Desktop I believe)
So theres a couple reasons so far as I know -
a: updating IE would in effect update Explorer and Explorer being apart of the OS, would require a system update - and most of us know how long it takes Microsoft to patch the OS.
b: for the longest time, Microsoft didn't care about adding new features. The browser wars of the time were over; IE won over Netscape and if theres no major competition, why spend the man power? Safari was never a threat to IE and it wasn't until Firefox came around and then Chrome did competition heat up a bit.
c: Microsoft was also very stubborn (and still is?). They wanted to push VBScript over Javascript. They had ActiveX components. Silverlight is roughly a competitor to Flash, etc...
I thought this was going to change with Edge. Edge was supposed to be a fresh start - a new, modern browser that could be updated on it's own, but I don't think that's true. People know a web browser on Windows to be Internet Explorer. Talk to any non-technical person about Edge and they'll look at you like you have 3 heads.
What should of happened was IE be removed completely from the OS; Edge made the standard and NOT integrated into the OS. Edge name change to IE and a team (I'm sure there is one) dedicated just to Edge development.
These problems of course all come down to target market - if your a startup targeting developers (for example) you can pretty much assume your market is not using IE or Edge. Students? Probably not IE or Edge. General population? Ie: a news website or browser games or general shopping site? Gonna need to target IE < 8 through Edge current.