Because you estimate a value, and you appraise a living being.
The "how many parrots" won't work if you don't explain what you are evaluating. "Estimating" asks about a number value, but you cannot say "I evaluate my children" to mean what you count them. This needs to be said and not implied.
If you estimate a quantity or value, you make an approximate judgment or calculation of it.
So, they use it only with "pretium/pretia", not beings.
If you appraise something or someone, you consider them carefully and form an opinion about them.
So it's applicable to beings (animals or human beings)
Notice that both appraise and estimate have the meaning of "considering carefully to form an opinion about it", but one is used for values, and prices, and the other one for living beings.
Well, it isn't any weirder than talking about angry drunk parrots.. at least some pet lovers may agree with the sentiment. ;) BTW. The connotation in English is not quite the same as in the romance languages. It's a bit more nuanced and it includes animals, on top of being an everyday word unlike inEnglish