"Which is why all our desktop apps are written in Java… Oh wait, they're not. The LibreOffice lot are even busy ripping Java out – not that I'm personally convinced that this is such a good move."
Eclipse & IdeaJ are two non trivial applications running on Java. And they're not just used for Java development either. Eclipse RCP is used in a raft of enterprise desktop apps. There are games too, of which Minecraft is the most well known.
"On the server-side Java got established in the corporate space and will remain for the duration But it wasn't because it was multi-platform, it's because it was what IBM, Sun, et al. were able to convince the suits to buy."
It was established server side because it is incredibly reliable and cross platform. Businesses value these things over raw throughput, Developers can write and package a .war / .ear application on a PC, transfer it to a suitable app server running on virtually anything and it will just work. It's extremely powerful and as testament to that, countless backends are powered by Java.
"As I said, the work done on the JVM has made it a lot easier for other languages to be reliably cross-platform. Also: thank god for QT!"
A QT application has to be recompiled, packaged, deployed and tested for every platform it runs on. It's no panacea.