Could alpha-numeric taxonomy of fungi make things simpler?
This is actually already done in some contexts.

For instance: yeast (a fungus) is a pretty extensively studied organism, and this means that there are a vast number of yeast strains which are know/used by biologists.  Many of these strains are referred to simply by an alphanumeric string rather than a "verbal" name.  (some examples in link 1)

This is also the case for bacteria, and maybe most of microbiology.