Why is Tk getting long in the tooth? This comment believes Tk is as good as wkWindows and QT https://news.ycombinator.com/item?id=12380456
Tk is limited, specifically, to being a gui toolkit, and even though the most recent versions look like native widgets, they are limited and the online support (from groups, etc) is limited. All the connecting libraries feel like you are back in the 90's programming again.
WxWidgets is to QT, as Linux is to Mac OS X -- one is cobbled together from amateurs with varying quality of components, and the other is built by professionals and held to professional rigor. The API (and output, in my opinion) is amateurish and dated in comparison. It lacks the polish and ecosystem that the professionally-supported QT has.
If you are making a full-fledged application (as opposed to a user tool or back-end interface) and are hell-bent on using a windowing toolkit (over say an HTML/CSS engine), then QT is currently the only correct answer. There are others around, but they all fall short of QT.
On a side note, Tcl (by the same original author as Tk) is a wildly under-appreciated scripting language.
What can Tk not do, specifically? This thread believes Tk is as good as QT https://news.ycombinator.com/item?id=12380456
http://forum.sqlitestudio.pl/viewtopic.php?f=16&t=334
That post is by the lead developer of a SQLite project competing with the one I'm involved in. The original version was developed in Tcl/Tk, and outgrew it.
Note - I'm not personally familiar with Tck/Tk, I just remembered reading this when you mentioned it. :)