Such numbering systems exist for many composers. Different scholars have created these catalogs, and so there are different organizational systems adopted.
In my mind, certain prolific composers, such as Vivaldi, would benefit
tremendously from a TWV-like catalogue.
I'm not certain from the wording of your question -- are you aware of things like the Ryom Verzeichnis (RV) numbering for Vivaldi's works? While it doesn't separate the numbering for key and subnumber as the TWV does, it does generally group works the same way, i.e., by genre, by instrument, and then by key.
Such scholarly catalogs and numbering systems exist for most major classical composers. (Vivaldi's works actually have at least three such scholarly catalogs, each with their own numbers.)
However, you are correct that not all such scholarly editions or catalogs of works group them in the same way. The standard numbering for Bach's works (BWV) is also grouped by genre, but, for example, the standard catalog for Mozart (Köchel Verzeichnis, or KV) attempts to number works chronologically. A major problem with the latter approach is that many works cannot be precisely dated, and later modified estimates for dating have led to numerous revisions of the KV numbers, often with appended letters to the numbers for works that have to be inserted in different places. Another problem shared by consecutive numbering systems from KV to BWV to RV is what to do with newly discovered works. Are they simply added at the end, thereby divorced in numbering from other works in their genre because of historical accident? Are they inserted (e.g., with appended letters or something to indicate their placement)? Is the entire catalog renumbered?
I agree that the TWV system avoids many of these problems, but we should remember that these works catalogs have developed over time as scholars have realized the various problems with previous numbering systems and tried to avoid the errors of those before them. The Köchel Verzeichnis for Mozart was first published in the 1860s and was one of the earlier attempts to number a composer's complete works. For Mozart in particular, there was also a particular interest in chronology (as he was known as a child prodigy, so it made sense to try to separate out his early works by numbering).
Nowadays, it's easy to look back and see the folly in trying to organize a catalog in such a fashion, but we stick with the KV numbers because they are already known and traditional. It's easier to publish a revised catalog with a few revised numbers rather than trying to get every edition of music out there to shift to completely different numbers for Mozart's works.
Consecutive numbering for all works (as in the BWV) became standard for a few generations, but it too suffers from problems and the need for renumbering.
Telemann was in some ways the benefactor of later scholarly interest. Although he was incredibly famous and influential in the 18th century (as well as a prolific composer), he fell by the wayside a bit compared to early scholarly interest in composers like Bach and Handel. The TWV numbering was only created and finalized in the 1980s and 1990s, so I think it benefited from hindsight in its numbering design. Some complete editions of works by other composers have adopted similar numbering systems in recent decades.
Even for scholarly editions that don't adopt a formal numbering system, a similar system to the TWV is often in place, where volumes are often numbered within genre first, and individual works are found grouped within those bands of volumes. These multitiered numbering systems are frequently used by scholars, but don't tend to appear much for referencing works outside of scholarly articles.
Unfortunately, as I said, the problem is that numbers like KV or BWV are so well-known that it's very difficult to propose a completely new numbering and supplant those numbers now, despite their flaws.
And of course for later composers (like Beethoven), a much higher percentage of their works were actually published during their lifetimes, so opus numbers become more important and relevant for convenient reference.
