It is not uncommon, among a certain type of readers of a certain age, to proclaim this book as, if not a favorite read... a seminal influence.

It certainly was for me. I owned it as a young person. Initially, it was a stubbornly avoided book with what I considered to be... an uninspiring cover. As a consequence, I would not pick it up. But when, finally,  I did--it's really not too much to say, "delight and wonder awaited." 
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The Sword in the Stone is, just as another enamored reader says, "an enchanted retelling of the childhood of King Arthur of England. The book's magical adventures, talking animals, and questing knights provide life lessons that foreshadow the rule of the most legendary king of all time." Yes. Enchanted--or enchanting--is definitely the word!

No one will ever claim that White was a master draftsman.  But the drawings are less dispensable than the modern publisher must believe. Certainly there are drawings that are cute, and add to the book's tone (especially for a young reader). There are humorous sketches of King Pellinore, anthropomorphized dishes washing themselves in a bucket--as if at a public bathhouse--along with the various animals that the Wart (future King Arthur) and his tutor Merlyn encounter on their adventures. But the drawings also included political references (a brutal giant appears, adorned with a swastika and the soviet hammer and sickle), and, more importantly, in early chapters they are directly referenced in the text. Merlyn tries to teach his charge about the confusions of living with "second sight" by having the Wart draw on a piece of paper--while looking only in a mirror. There is a one way that these drawings can be laid out properly on a modern typeset page--and clearly the paperback edition of TSitS I am reading from (which follows the beloved 1938 version of the text) didn't bother to set it up that way.  I had to crop together pictures from two pages to demonstrate how badly Wart manages it.

This is a book I have reached for through decades. In the 1990s, at least, the publishers honored White's inventive play. Perhaps King Pellinore and the playful dishes were gone, but the M (which should have been a W) and this delightful page were included, in which Merlyn attempts to conjure up his own pointed wizard's hat, and ends up shrieking, in an sulky passion, "This is an anachronism! That's what it is, a beastly anachronism!"

Modern publishers evidently know better, eliminating the intertextual illustrations (and the expense of producing them).

But what remains?

A book... which has been stripped not only of its humor, but of its capacity to be comprehended.

So--what this post is saying: I fear that ​The Sword in the Stone is lost to us as readers.

The archetypal nature of the icy grandfather, ceding way to his more delicate grand-daughter--who melts away in spring, cycling back to repeat out of the depths of each winter... it feels to me that something deeper (and older) is at work here than a late Imperial Russian fantasy.

I'm reading the "New and Revised" edition of 1919. My understanding is that there's a good, more recent, complete e-edition out (from Fonthill Press), an edition which restores all the "rampantly expurgated and cleansed" bits that her mother took out before allowing the work's publication.

Oh yes. Given the mischief I've read already on the page, I'm definitely intrigued to dip into Fonthill's unexpurgated bits, but... I'm also curious about the text that became a bestseller in Europe in 1887 (three years after Bashkirtseff's death)--the text, evidently, that held a beloved place of pride on the shelves of many a young educated woman of a certain class in the years before and after WWI.