Why is locking a std::mutex twice 'Undefined Behaviour'?

Solution 1:

Because it never happens in a correct program, and making a check for something that never happens is wasteful (and to make that check it needs to store the owning thread ID, which is also wasteful).

Note that it being undefined allows debug implementations to throw an exception, for example, while still allowing release implementations to be as efficient as possible.

Solution 2:

Undefined behavior allows implementations to do whatever is fastest/most convenient. For example, an efficient implementation of a non-recursive mutex might be a single bit where the lock operation is implemented with an atomic compare-and-swap instruction in a loop. If the thread that owns the mutex tries to lock it again it will deadlock because it is waiting for the mutex to unlock but since nobody else can unlock it (unless there's some other bug where some thread that doesn't own it unlocks it) the thread will wait forever.