Pottery kilns seem like a special case. Most kilns gets much hotter and also have pottery treated with chemical glazes that could skew the chemical composition of the ash. It seems illogical to assume ash from a potter's kiln is the same as ash from a hearth. However, I appreciate your concern for the animals and agree that just because something is common practice does not make it safe or good.
As a person also dedicated to science, I decided to put wood ash to a pH test. I used Cardinal Health SP pH indicator strips from the university chemistry department. These strips have a test sensitivity of 1 pH and a range from 0 - 14. I tested wood ash in three forms: straight out of the fireplace with less than 6 hours of rest, day old ash, and ash mixed in to dirt in the yard (where the ash was still a large enough component of the mixture to make the dirt look grey). All of the ash was taken from my home fireplace where I burn wood from a pecan tree that recently died. I mixed 1 Tbsp of dry ash or ash mixture with 3 Tbsps of water in a pyrex glass test tube. The results of the test are as follows: fresh ash has a pH of 11, day old ash had a pH of 10, mixed ash has a pH of 9. My soil naturally (untreated by ash or fertilizer) has a pH of 8 to 9. I performed each pH test twice to increase accuracy. A test size of 2 is small but quality pH paper is not cheap. The results seems to suggest that while ash is high on the pH scale when fresh by the time it has rested and mixed with dirt it is not so caustic as to be of immediate alarm. I would be interested to see what pH other types of wood and/or soil conditions produce.