It is usually wise to trim books when they are rebound. But this trimming should of course be as little as possible.
Showing the Method of Lacing in the Slips or Ends of Bands on a Flexible Bound Book
If depressions are cut in the board as shown, the slips can be left with an adequate margin of strength without clumsiness.
From report of the Committee on Leather for Bookbinding. Edited for Society of Arts. London: Bell & Sons, 1905.
It is possible to whipstitch a book, even one which is printed on stiff paper, in such a way that it will be almost as flexible and open almost as easily as if it were sewed on tapes in the regular way. It is possible, but difficult. Few have done it. Few binderies, if any, in this country have workers who can and will give to the work of whipstitching the care and thought necessary to produce a good job.
No. 1
No. 2