...But it is, quite frequently, a tool of the poet.
In poetry, white space (not just between verses, but after each line ends) is used for a variety of reasons. Actual, physical readability is only the tip of the iceberg.
Rhyme, meter (scansion), enjambment, and other qualitites of verse are dramatically enhanced by the use of white space. The space left on the page acts as a pointer, drawing a given reader's attention to the lines themselves, and causing them to look for reasons why the poet did not make the lines fill up the entire page. Line breaks are crucial to poetry; a poet may have any number of reasons for ending lines at x location. White space then makes the reader look more closely at the few words available, and to draw as much meaning as possible from this limited amount of data.
For example, take William Carlos Williams's poem, Tract. The first stanza runs as follows:
I will teach you my townspeople
how to perform a funeral--
for you have it over a troop
unless one should scour the world--
you have the ground sense necessary.
Look at the line breaks; look at the lines themselves and ask yourself why Williams is breaking these lines in these specific places. There is no direct rhyme here, no overt meter, but there is a carefully planned set of words, set out in this fashion for a reason. For instance, take "townspeople" and "troop": these two words are alliterative (the T sound) and consonant (the P sound). We are used to looking at the end of lines for a rhyme; here Williams does not use a rhyme, but he uses similar sounds, shortening one word into another in order to enhance the similarity he wishes to draw between them.
The short line "of artists--" provides a great deal of white space for the reader to work with. Why leave the line so short? Why leave so much space after it? The active word in the line is "artists"; perhaps Williams wants to emphasize that funerals should be performed in the same way that an artist (in this case, perhaps an acting or acrobatic troupe) performs.
Look at the last line, as well; why does Williams break his stanza after "ground sense necessary"? Could it be that he wants his readers to pay closer attention to these ending words? The word "necessary" has more syllables than any word thus far; this draws attention to it. The consonant conjunction with the previous word (the S sound) draws more attention to it. But the fact that it is the very end not only of a line but a stanza makes the line itself very important within the body of the poem. The sense Williams sees as necessary for decent funerals is what he wants to emphasize here; both the sense to perform as artists and the necessity of this sense are highlighted.
As for physical readability, short lines may make poems easier to read than long; I can think of some lines in The Faerie Queene and Paradise Lost which are so long you forget what's going on by the time you get midway through. You should rarely encounter this problem in short lines. However, keep in mind that poets may choose to un-use white space as well. Sometimes the effect a poet wants is of overcrowding, of confusion. What better way to confuse people than to make them lose their place in a poem? Why not fill up the page entirely, overflowing the margins? Why not use the Tristram Shandy effect, and fill a page entirely black with ink because there is just so much to say about a given subject?
In short, the use of white space draws more attention to the lines themselves, and why they are the way they are. Poetry pays close attention to economy of language; each item in a given poem is (or should be) used for a specific reason. The overuse of words is done for a reason as well. The words are charged; the white space is also charged. What is unsaid is as important as what is said.