All this time I had been assuming that threads were automatically
running concurrently on multiple cores but I've recently discovered
that you actually have to explicitly code for handling multiple cores.
The above is incorrect for any widely used, modern OS. All of Linux's schedulers, for example, will automatically schedule threads on different cores and even automatically move threads from one core to another when necessary to maximize core usage. There are some APIs that allow you to modify the schedulers' behavior, but these APIs are generally used to disable automatic thread-to-core scheduling, not to enable it.
So what's the point of multi-threading on a single core?
Imagine you have a GUI program whose purpose is to execute an expensive computation (for example, render a 3D image or a Mandelbrot set) and then display the result. Let's say this computation takes 30 seconds to complete on this particular CPU. If you implement that program the obvious way, and use only a single thread, then the user's GUI controls will be unresponsive for 30 seconds while the calculation is executing -- the user will be unable to do anything with your program, and possibly unable to do anything with his computer at all. Since users expect GUI controls to be responsive at all times, that would be a poor user experience.
If you implement that program with two threads (one GUI thread and one rendering thread), on the other hand, the user will be able to click buttons, resize the window, quit the program, choose menu items, etc, even while the computation is executing, because the OS is able to wake up the GUI thread and allow it to handle mouse/keyboard events when necessary.
Of course, it is possible to write this program with a single thread and keep its GUI responsive, by writing your single thread to do just a few milliseconds worth of computation, then check to see if there are GUI events available to process, handling them, then going back to do a bit more computation, etc. But if you code your app this way, you are essentially writing your own (very primitive) thread scheduler inside your app anyway, so why reinvent the wheel?
The first versions of MacOS were designed to run on a single core, but had no real concept of multithreading. This forced every application developer to correctly implement some manual thread management -- even if their app did not have any extended computations, they had to explicitly indicate when they were done using the CPU, e.g. by calling WaitNextEvent. This lack of multithreading made early (pre-MacOS-X) versions of MacOS famously unreliable at multitasking, since just one poorly written application could bring the whole computer to a grinding halt.