There are numerous applications that satisfy your criteria, you have just written them to sound daunting. Just about any image processing application (photoshop, gimp) or video or audio application is a candidate. If you don't have needs for real multi-threading, then lucky you, but many people do.
The GIL is a huge wart of the side of an otherwise attrective language.
This needs to be fixed for the language to be taken seriously. Otherwise Python will be consigned to the scrap heap of toy languages like Pascal. It's not even worth debating it. Don't rationalize this wart, think about how it could be fixed.
I came to love python and teach classes in it. Now, due to frustration over the GIL (i.e. the fact I could double or octuple) the speed of the compute-bound processing I do, I may switch back to C or Java for my own work.
To call this a "corner case" is just silly. The popularity of multi-core systems is not just for running multiple process. Multi-threading is often much easier to implement for a computationally intensive task.