Traditionally, the Torah is divided into paragraphs and sub-paragraphs graphically and is seen as being meaningfully categorized as such. As the Rambam codifies, the validity of a Torah scroll is dependent upon the correct graphical structure of the text.
In virtually all modern Chumashim, commentaries and Jewish publications, the reference numbers used are what we called Perakim, which were introduced by the Christians. This numbering system gained usage for a number of reasons, but much more with the advent of mass printing, especially since many early printers were Christians. The numbering of verses according to chapters wasn't done until 1551.
Sorry for the lengthy introduction. I believe that using a Chumash which follows the structure of Torah through the correct breakdown and organization is useful for a Jew to gain an understanding of how the Torah is meant to be laid out.
Are there any Chumashim in publication today which number the graphical paragraphs and sub-paragraphs as the main method of navigation for the Chumash? For example, a verse in the third Setuma of the second Petucha of a Sedra might be ז(ג):יד, or what have you?