Someone who buys a lot of books but barely reads them

Solution 1:

Consider, bibliomaniac/bibliomane

bibliomania: excessive fondness for acquiring and possessing books Random House

bibliomane: one who passionately collects books Classic Used Books

Solution 2:

You may be interested in the Japanese word tsundoku 積ん読:

(informal) the act of leaving a book unread after buying it, typically piled up together with other such unread books

Solution 3:

One Word

One thing or the other, either a book collector or somebody who doesn't read often, can be found...but both those denotations in one word is a taller order. The closest I could come was

bibliotaph, n.
One who buries books by keeping them under lock and key.

["bibliotaph, n.". OED Online. December 2015. Oxford University Press. http://www.oed.com/view/Entry/18650?rskey=NbAjB9&result=65&isAdvanced=false (accessed December 28, 2015).]

One must have books in order to bury them by locking them away, of course, but that's not to say the bibliotaph loves to buy and collect books.

Two or More Words

Although the OP is a single word request, perhaps a well-formed noun phrase would do. Given the lack of a single word that covers the desired sense, perhaps a noun phrase is necessary. So, I'll suggest a

somewhat aliterate bibliotaph.

'Aliterate' is not a rare adjective. It is found in, among others, American Heritage, Collins, Random House Kernerman Websters, and the OED Online, as well as garnering about 24,000 hits on Google. The OED Online defines the adjective as

  1. Of a person or group: unwilling to read, although able to do so; disinclined to read.

["aliterate, adj. and n.". OED Online. December 2015. Oxford University Press. http://www.oed.com/view/Entry/240391?redirectedFrom=aliterate (accessed December 30, 2015).]

As shown, I would use 'somewhat aliterate', because the sense I understand from the description of the intended use by the OP is less extreme than entirely disinclined, and the book collector described is not unwilling (other than circumstantially) to read.

'Aliterate' or 'somewhat aliterate' could also be used to good effect with words suggested in other answers than this. For example,

  • a somewhat aliterate bibliophile, or
  • a somewhat aliterate bibliomane.

Obsolete and Obscure Words

An obsolete sense of bookkeeper perhaps comes closer:

†2. A person who hoards books. Obs. rare.
....
1788 F. Grose Classical Dict. Vulgar Tongue (ed. 2) Book-keeper, one who never returns borrowed books. 1833 Humourist's Own Bk. 46 Sir Walter, in lending a book one day to a friend, cautioned him to be punctual in returning it... ‘For though many of my friends are bad arithmeticians, I observe almost all of them to be good book-keepers.’
1884 Harper's Mag. Nov. 828/1 The old-fashioned book-keeper, who fears his precious books will be hurt by using.

For the sense you requested, see especially the 1884 quote regarding the bookkeeper

... who fears his precious books will be hurt by using.

["bookkeeper, n.". OED Online. December 2015. Oxford University Press. http://www.oed.com/view/Entry/21437 (accessed December 28, 2015).]

In the region of the entirely obscure, although not obsolete, there is the uncut man:

c. transf. Given to collecting ‘uncut’ books.
1862 J. H. Burton Bk.-hunter (1882) 19 He was not a black letter man or a tall copyist or an uncut man.

This adjective applied to persons by way of the transferred sense draws on the sense of uncut applied to books:

a. Of books: Not having the leaves cut open.

Two camps or schools of thought on the 'cutting' of book leaves exist, though: one maintains an 'uncut' book does not have its leaves cut open; the other maintains an 'uncut' book does not have its margins reduced.

b. Not having the margins cut down.

In that sense (sense b), how easily the book may be read is irrelevant; in the other sense (sense a, shown above, manifest in persons as sense c, also shown above), while it is possible to peer down between the uncut leaves, it is quite difficult to read an uncut book.

["unˈcut, adj.". OED Online. December 2015. Oxford University Press. http://www.oed.com/view/Entry/211145 (accessed December 28, 2015).]