Sure, as a physicist, I have written papers with pseudocode for algorithms, and I think we would do well to express algorithms in this way. That's definitely an improvement that is slowly percolating various fields. But most mathematical theorems and their proofs are not algorithms, and not suitable for expressing this way.

The reason for single-letter variable names is that mathematics is best learned by manipulating ideas by hand on paper and pen. And that many mathematical expressions are long and if we started using longer names, we would end up writing only a couple of statements per page, which would be much annoying than just using symbols.