Why must/should UI frameworks be single threaded?

TL;DR

It is a simple way to force sequencing to occur in an activity that is going to ultimately be in sequence anyway (the screen draw X times per second, in order).

Discussion

Handling long-held resources which have a single identity within a system is typically done by representing them with a single thread, process, "object" or whatever else represents an atomic unit with regard to concurrency in a given language. Back in the non-emptive, negligent-kernel, non-timeshared, One True Thread days this was managed manually by polling/cycling or writing your own scheduling system. In such a system you still had a 1::1 mapping between function/object/thingy and singular resources (or you went mad before 8th grade).

This is the same approach used with handling network sockets, or any other long-lived resource. The GUI itself is but one of many such resources a typical program manages, and typically long-lived resources are places where the ordering of events matters.

For example, in a chat program you would usually not write a single thread. You would have a GUI thread, a network thread, and maybe some other thread that deals with logging resources or whatever. It is not uncommon for a typical system to be so fast that its easier to just put the logging and input into the same thread that makes GUI updates, but this is not always the case. In all cases, though, each category of resources is most easily reasoned about by granting them a single thread, and that means one thread for the network, one thread for the GUI, and however many other threads are necessary for long-lived operations or resources to be managed without blocking the others.

To make life easier its common to not share data directly among these threads as much as possible. Queues are much easier to reason about than resource locks and can guarantee sequencing. Most GUI libraries either queue events to be handled (so they can be evaluated in order) or commit data changes required by events immediately, but get a lock on the state of the GUI prior to each pass of the repaint loop. It doesn't matter what happened before, the only thing that matters when painting the screen is the state of the world right then. This is slightly different than the typical network case where all the data needs to be sent in order and forgetting about some of it is not an option.

So GUI frameworks are not multi-threaded, per se, it is the GUI loop that needs to be a single thread to sanely manage that single long-held resource. Programming examples, typically being trivial by nature, are often single-threaded with all the program logic running in the same process/thread as the GUI loop, but this is not typical in more complex programs.

To sum up

Because scheduling is hard, shared data management is even harder, and a single resource can only be accessed serially anyway, a single thread used to represent each long-held resource and each long-running procedure is a typical way to structure code. GUIs are only one resource among several that a typical program will manage. So "GUI programs" are by no means single-threaded, but GUI libraries typically are.

In trivial programs there is no realized penalty to putting other program logic in the GUI thread, but this approach falls apart when significant loads are experienced or resource management requires either a lot of blocking or polling, which is why you will often see event queue, signal-slot message abstractions or other approaches to multi-threading/processing mentioned in the dusty corners of nearly any GUI library (and here I'm including game libraries -- while game libs typically expect that you want to essentially build your own widgets around your own UI concept, the basic principles are very similar, just a bit lower-level).

[As an aside, I've been doing a lot of Qt/C++ and Wx/Erlang lately. The Qt docs do a good job of explaining approaches to multi-threading, the role of the GUI loop, and where Qt's signal/slot approach fits into the abstraction (so you don't have to think about concurrency/locking/sequencing/scheduling/etc very much). Erlang is inherently concurrent, but wx itself is typically started as a single OS process that manages a GUI update loop and Erlang posts update events to it as messages, and GUI events are sent to the Erlang side as messages -- thus permitting normal Erlang concurrent coding, but providing a single point of GUI event sequencing so that wx can do its GUI update looping thing.]