Do you have any support for your position that that is a poor spelling? There are multiple ways in active use of transliterating Japanese. One of them involves writing shi+i as shii to produce shiitake, which is then left as is. Another one of them involves writing shi+i as shī to produce shītake. As ī involves a marker English does not have, it gets dropped when used in English. Both make sense.

The dictionary’s job is to describe you how words are used, not prescribe definitions.

Unfortunately it is often cited for the latter purpose.