This article would be much better if it had some data and evidence. A quick check on google ngrams reveals that the phrase 'well kempt' surged in popularity after 2000, relative to the two previous centuries. 'Unkempt' is still far more popular, but 'kempt' has by no means disappeared.
On the other hand: "kempt" primarily survives as the fixed phrase "well kempt", and hasn't retained its original meaning as the past tense of "to comb".
