What we needed to see is the EMH hovering over one injured crew member while his 7 arms are snaked out all over sickbay attending to multiple other injured crew members (which he can see through his hands). Because he totally could do this.
Undoubtedly. The question is, though, should
he? How many humanoid types would feel comfortable with what amounts to an Elder God (or at the very least, a Thermian) waving wandage in their faces?
Again, we keep with what is comfortable & familiar so as to soothe the senses despite the enhanced abilities & efficiencies of modified types. Otherwise, why not just make the EMH take the form of sentient holographic gas? That would certainly be the most efficient diagnostic form.