Late answer, but I think it adds something new to this topic.
None of the previous answers has answered the original question. Some have attempted to justify the lack of a constant, while others have showed ways in which we can deal with the lack of the constant. But no one has provided a compelling justification for the benefit of the constant, so its lack is still not properly explained.
A constant would be useful because it would prevent certain code errors from going unnoticed.
Say that you have a large code base with hundreds of references to "". Someone modifies one of these while scrolling through the code and changes it to " ". Such a change would have a high chance of going unnoticed into production, at which point it might cause some issue whose source will be tricky to detect.
OTOH, a library constant named EMPTY, if subject to the same error, would generate a compiler error for something like EM PTY.
Defining your own constant is still better. Someone could still alter its initialization by mistake, but because of its wide use, the impact of such an error would be much harder to go unnoticed than an error in a single use case.
This is one of the general benefits that you get from using constants instead of literal values. People usually recognize that using a constant for a value used in dozens of places allows you to easily update that value in just one place. What is less often acknowledged is that this also prevents that value from being accidentally modified, because such a change would show everywhere. So, yes, "" is shorter than EMPTY, but EMPTY is safer to use than "".
So, coming back to the original question, we can only speculate that the language designers were probably not aware of this benefit of providing constants for literal values that are frequently used. Hopefully, we'll one day see string constants added in Java.