The term "song" in the Work Type list refers to form, not content. Whether or not something has vocals or lyrics is something that something that should be documented somewhere other than the Work Type field. I pointed this out, and you accused me of wanting to deprive future generations of the ability to find instrumental compositions. If you want a serious reply, please stick to serious arguments.
A few methods have already been discussed. I'd prefer to add it as an attribute, but currently you have tags and can set the lyrics to [no lyrics].
There isn't even consensus over what constitutes an Instrumental. Is it based on vocals or the presence of lyrics? Is "Fitter, Happier" an instrumental? It has words, but no vocalist. Is "Great Gig in the Sky" an instrumental? It has vocals, but no lyrics.
They didn't classify it as an established form because it wasn't an established form. "Solo piano" is descriptive information, not a statement of form or even genre. (FWIW, "Images" was a series of works, not just the solo piano pieces in sets 1 and 2. Set 3 was orchestral.]
You're interpreting the word "song" as meaning "with vocals" and trying to create something that covers everything outside of that category. But the presence of singing alone does not make something a song. A mass is not a song. Beethoven's 9th is not a song. Einstein on the Beach is not a song, either in whole or the individual movements. "Song" is used ubiquitously with rock music because that's overwhelmingly the most common form in in the genre, though it's not always correctly used.
You're both talking about genres, styles, and performance techniques, not forms. "Blues" is not a form; a "blues progression" is a form that can be used in any genre. "Baroque" is not a form; if you wanted to write a Baroque piece, you'd probably choose one of the common forms they used. You may have written "jazz" on one of your compositions, but if somebody played the notes on the page in a rock style, it's still the same work; you may not want the performers to choose the style of performance, but ultimately they can. And before you say "then it's not the same work", would you refuse a royalty check?
Oh, and if we're brandishing our credentials here, I have a PhD in composition, so I've done my fair share of musical analysis.