Until the 19th Century, all books were printed on hand-made paper. To over-simplify, hand-made paper is produced by pulling a wire screen through a vat of fibre slurry to pick up exactly the amount of fibre to make one sheet of paper. To confine the spread of the fibres on the screen, and control the thickness of the loose fibres deposited on the screen, there is a (removable) frame around the surface of the screen. This frame in called a deckle.
Inevitably, a little fibre leaks under, and is trapped by, the deckle. When the frame is removed and the wet sheet of fibre is laid off on a stack with blankets, (to be pressed to remove the water), the ragged edges of the sheet, caused by the fibres which "leaked", remain on the sheet all through the drying process. These edges are called, - ta-da! - deckle edges.
It was extremely inefficient to cut these edges off sheets of paper before printing and binding. Originally, printing presses did not require that paper have even one smooth edge in order that all the sheets be printed (in register) uniformly. (From the 19th Century on, they did, but that history is a different subject). So, books were printed on these deckled sheets, then they were sewn up, and if desired, the deckles were planed off the top, and/or fore-edge and/or bottom of the book just before the covers were built on. Sometimes the book required a smooth top for gilding, for example, or a smooth fore-edge for decorating, etc.
With antiquarian books, it is extremely important that a book have exactly the form in which it was published. If it was published with a deckled fore-edge, it must remain that way, or the value will plummet. Re-binders are notorious for trimming without permission -- these heretics must be warned that there is an extremely deep level of Hades reserved for them!
Beyond the period when deckled edges were an automatic by-product of paper production, publishers continued with the convention of publishing their best books with deckled edges, and paper-makers accommodated them with machine-made paper on which at least two edges were deckled. (They still do.) While this was something of a conceit, it was still a mark of quality in that it imitated the hand-made look and indicated higher cost paper and handling. (Binding books to preserve their deckled edges is more difficult.)
So, in the late 19th and early 20th Centuries, books continued to be published with deckled edges to identify quality paper and near hand-made production. Hence, with books of that period, leaving the deckled edges alone preserves that original mark of quality as well as the proof that the book has not been altered from its original state. This is very important to collectors and is thus essential if you ever expect to sell the book.
Presently, limited edition books, books from private presses (still hand-made and another whole different subject) and books their commercial publishers want to make seem of high and collectable quality, are still being published with deckled edges -- and sometimes with hand-made paper where the deckled edges are very definitely not a conceit.
The main problem with deckled edges is not that they are harder to page through, but that they trap dust. Accordingly, re-binders are often asked to trim the tops of books to facilitate dusting. Re-binders can do it, because the covers will have been removed. An owner, however, is not going to be able to do a respectable job of trimming pages so that they are uniform. This would quite frankly be the ruination of the book. Trimming fore-edges might seem easier, but because of the curve of the back, uniformity even in doing that would be near impossibility with a bound book.