What is the origin of the idea that the word "able" must refer to a living being?
Solution 1:
Note : I have not (yet) managed to find an instance, before Heffer, of a quibble being voiced regarding the attribution of 'ability' to a non-living thing but I have managed to find an instance, earlier than Wilson, of 'ability' being attached to a non-living thing.
The land being 'not able' to bear Abraham and Lot.
The earliest example of 'ability' attributed to a non-living thing that I have yet found is a comparison between the Coverdale Version of the bible (1535) and the Wycliffe translation of 1382 of the text regarding Abraham and Lot (Genesis 13:6).
The Textus Receptus Interlinear
The Coverdale is quite happy to say that :
so yt the londe was not able to receaue them, that they might dwell together: for the substaunce of their riches was so greate, that they coude not dwell together. [1535].
But The Wycliffe, 153 years earlier, has not so stated the matter :
and the lond miyte not take hem, that thei schulden dwelle togidre, for the catel of hem was myche, and thei miyten not dwelle in comyn. [1382].
After the Coverdale, the Matthew Bible (1537), The Great Bible (1539) and the King James Authorised (1611 and 1769) all have 'the land was not able to bear them'.
So as far back as 1535 English was content to say that a thing was able - or 'not able' - to perform a function.
Solution 2:
I do have a certain amount of sympathy with Simon Heffer here.
Saying that a person "is able", or "is unable", suggests (to my mind) that some sort of effort, physical or mental, is involved.
So, since an inanimate object is incapable of making an effort, then "the key is able/unable to unlock the door" is metaphorical. Whether the key unlocks the door or not is a question of fact, not one dependent on ability.
One could though say that "the dog was unable to climb over the fence" - since dogs do make efforts to do such things, sometimes with success, sometimes without.