I would like to suggest another way of looking at this problem.
Perhaps we can distinguish between those "animals" the Professor was careful to tie into the overall Legendarium and those he was not.
In the former category are the Great Eagles, the spiders, and Huan. In the latter we can find a talking thrush or a sentient fox. My gut feeling is that these originated from different places in Tolkien's imagination.
The book The Uncharted Realms of Tolkien goes into great detail showing how there were certain elements in the writings that the author purposely did not tie into the Silm. Chief among these was Tom Bombadil. Except for the early poems (that weren't published till later) and LotR itself, Tom is missing from both the Silm and UT. This stands in sharp contrast to other elements introduced in LotR. The
istari , for example, and also the Ents -- these were also new but the author was careful to reintroduce them to Silm and/or UT to show exactly how they fit into the larger scheme. This stands in sharp contrast to Tom who simply does not appear. According to Uncharted Realms, the origin of Tom does not lie in Middle-earth per se, but rather in the English countryside, its legends, folklore, and spirits.
Can we not say the same thing about the animals? I get a wholly different feeling from the Eagles than I do from the small thrush in the Hobbit. To me, the fox and the thrush are a natural outgrowth of the countryside. They are part of the "natural" and "folk" elements: the same kind of character we see in Wind in the Willows. This stands in sharp contrast to something like the dragons or Eagles. Whether they are maia or not is open to question, but they have a "greatness" about them (as do the spiders) which makes them more than simple country animals or an aspect of British folklore.
There is an interesting side question here that Littlemanpoet has raised on several occasions. To what extent do hobbit origins lie in the "animal" side of things: the celebration of the natural? Both rabbits and badgers have been put forward as models. If we choose to see hobbit origin in this way,( and Uncharted Tales makes a fascinating argument for Badger origin,) then the Hobbit is the ultimate talking animal,

, one whose roots in the countryside and folklore run deep yet who still makes it into Silm: a unique amalgamation!