@CBR: Having 2 accounts and using "favorite" kindles and Fire's we were always swapping accounts and having to download books and generally getting into a terrible muddle and kicking off restarts and indexing left, right and center. Got used to having to do Factory Default settings regularly just to keep track.
Since the Family Library thing there is no longer a need to swap devices and do not remember seeing indexing on the beloved Gen3 Keyboard Kindle in ages other than for new load new books.
Perhaps everything has moved on and this is now one of the "Urban Myths" that need to die out gently :)
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Well, I finally spoke to the Kindle tech support people, they agreed that it should not be doing this and sent me a replacement. So far it has performed much better, even the indexing did not seem to take as long as on my old one. The battery drain is also much more on a par with what I have come to expect so it looks like it was a faulty unit.