Huffman Code VS Hu–Tucker Code

Question

Before I'll ask my question, let me start with my understanding of the definitions, to prevent myself with further confusion, as well as giving some background.

Huffman Code is the binary-code induced from a binary tree, constructed by Huffman's Algorithm.
Hu–Tucker Code is the binary-code induced from an alphabetical search tree.
According to Wikipedia (see the paragraph on Optimal alphabetic binary trees (Hu–Tucker coding)):

In the standard Huffman coding problem, it is assumed that any codeword can correspond to any input symbol. In the alphabetic version, the alphabetic order of inputs and outputs must be identical. Thus, for example, $A = \left\{a,b,c\right\}$ could not be assigned code $H\left(A,C\right) = \left\{00,1,01\right\}$, but instead should be assigned either $H\left(A,C\right) =\left\{00,01,1\right\}$ or $H\left(A,C\right) = \left\{0,10,11\right\}$. This is also known as the Hu–Tucker problem, after T. C. Hu and Alan Tucker, the authors of the paper presenting the first linearithmic solution to this optimal binary alphabetic problem, which has some similarities to Huffman algorithm, but is not a variation of this algorithm. These optimal alphabetic binary trees are often used as binary search trees.

My question is, what are the applications of such trees? (alphabetic binary tree)
I tried to search online, but couldn't find a satisfying answer.
I also read the introduction in Hu & Tucker's paper on the subject: Optimal Computer Search Trees and Variable-Length Alphabetical Code, but I couldn't figure out exactly the use of such tree from their example.

I can very well understand the need of a compact, optimal prefix code, induced by an optimal tree (i.e. Huffman Code); this can be used for compression, but what is the use of alphabetical binary trees?