First of all, there are some important differences between horizontal and vertical lines, which all eventually originate from the pertinent writing systems being horizontal and not vertical.
It is standard to arrange tables such that the same type of information is arranged in columns, not rows. This in turn is because in a horizontal writing system, it is better to align similar information on top of each other instead of next to each other. As a result, the majority of academic tables have distinct index rows (a.k.a. header rows), but no index columns. By distinct, I mean that they contain a totally different type of information, e.g., “weight” as opposed to “5 kg”. It makes sense to separate these index rows visually by a horizontal line. (This line also serves as a visual indicator that the agglomeration of characters you are viewing is a table.)
Since the height of rows is usually much smaller than the width of columns in a horizontal writing system, readers are much more prone to jump across rows than columns. Further, the aforementioned predominance of columns makes it often easy to notice if you are in the wrong column. Thus, while horizontal lines may be called for for eye guidance occasionally, vertical lines hardly ever are.
In many academic contexts, it is common to have footnotes below a table. To separate these, it makes sense to add a horizontal line at the very bottom. In a horizontal writing system, we usually wouldn’t put something like footnotes on the side of a table.
In my experience, the vast majority of academic tables need exactly one line, namely to separate the index row (header) from the body. A horizontal line at the very bottom can be added as a stylistic choice or to separate footnotes or similar. Everything else is unnecessary and visual clutter. There are rare occasions where more lines, sometimes even vertical ones, are called for, but those make up for far less than one percent.
Also, in my experience, most academics tasked with formatting a table will use every line they possibly can, resulting in badly readable tables. Thus, I can fully understand that publishers radically restrict line use in their rules as a default. The same publishers may even accept vertical lines, if the authors can argue that their particular table requires them. So, this rule may not be cast in stone, but presenting it as if it were is the lesser evil.
you could easily construct little-horizontal-space examples where line removal makes columns hard to separate visually, or where table columns are grouped and groups have to be visually separated.
I would guess that even in the majority of these special cases, you end up with a better table if you first force the authors to work without vertical lines and think of better ways to present the data, e.g., by reducing the need for horizontal space or visually separating groups otherwise.