Moreover, even common practice harmony doesn't include all the tools needed to analyze the harmony of the common practice period, but we get by. For example, in the first movement of the Symphony in G minor, K. 550, Mozart inverts the motive toward the end of the development section over a dominant pedal and harmonizes the initial lower chromatic neighbor of that three-note motive. So you get a fully-diminished 7th chord built on d that is immediately followed by a dominant seventh build on d. What do you call that fully-diminished 7th chord in Roman numeral analysis? Perhaps there's a standardized name or symbol for this now, but even if that's the case there wasn't always. But it didn't matter because you could trivially come up with something like calling it a "neighbor seventh" or some other such name and everyone would know what you are talking about because 18th- and 19th-century music was full of that chord progression.
Now look at, say, the opening to Prelude to the Afternoon of a Faun. Debussy's solo flute solo holds a note over the ensemble playing the first chord of the piece-- a half-diminished 7th chord. This sounds similar to the beginning of the Tristan Prelude cellos when they hold a note over a half-diminished 7th chord. But unlike Wagner, Debussy has it resolve to a dominant seventh on the same root as the half-diminished seventh. (In fact, I'm not sure Wagner ever used that progression to resolve the Tristan chord throughout the entire opera.)
Just as we could talk about the function of that same chord progression in Mozart without a name for the "neighbor seventh," so too can we do it in Debussy. It just so happens there are a lot more harmonic shifts in the Debussy to talk about, so its more work, added to a discussion of the various allusions to Wagner and how they come off.
I guess having some common language for discussing the historical development of octatonicism would help in this case. Still, this was an experimental time in harmony with a lot of bespoke forms. I'm not sure how much a common extended toolset would add to any given piece. (Not to mention you had your Rachmaninoffs and others who are almost fully analyzable using Roman numeral analysis and tonal chromatic voice leading.)
Edit: clarification