IE is not a stand alone browser. IE is built on top of dozens of different Windows components. In order for IE to be open sourced you would have to open source a large chunk of Windows itself, the two aren't that inseparable.
You could definitely open source the UI, but the UI in IE is fairly light weight, most of the actual useful stuff is not within it and providing the UI source would likely not really offer much.
Another useful question to ask is, let's say they do open source all of the components, then what? Windows enforces Microsoft signing and other checks on internal components for security reasons. So if you compiled a new copy of e.g. http.sys you likely couldn't install it anyway.
Plus they'd have to audit the heck out of the code before doing so for IP issues. It would be very easy for every patent troll to point at lines within IE's code and then sue.
I see it lacks a mention to the embedded PDF reader which, if I remember correctly, is licensed from Foxit.
This company is a new company, and I personally am paying a lot of attention to it having been a hater for a long time. The latest IE is a decent effort if you leave out Bing (which remains awful) and open sourcing it should be encouraged and applauded if it were to occur. As much as I love Firefox, IE is in my experience a far more stable and credible long term competitor to Chrome. For an example of some of the unsung quality behind IE, it is the ONLY browser that sends SVGs to a printer as vectors and not a screen-raster rendering. This is a small detail but points, to me, to the underlying quality that IE represents. For other Microsoft doubters: typescript, or the almost single-handed effort that Microsoft has put in to defeating large botnets.
Microsoft has track record by not making smart choices.
Also, we don't really need the entire application open-sourced. There might be an argument to be made for open sourcing Trident (the rendering engine), but only for the purposes of figuring out what in the hell is happening under the hood that's causing things to work so poorly. If any part of IE were open sourced, I imagine that at least modern versions of it are written on top of .NET which is also open source now, so maybe it would be made to work on multiple platforms? This is a bad thing. As I said before, we need less IE, not more.