Recipe filter by professions currently only show the recipes of the professions that the current character have, but in the case of Engineering the recipes are not filtered based on the specialization, so the recipes of the other specialization are marked as incomplete even it is impossible to learn them.

In BFA this is only a problem for Engineering because Alchemy does not have any recipe based on specialization but in Classic this will happen too with Blacksmithing, Tailoring, and Leatherworking specializations.

You are making your claim that 100% is possible on one character if I introduce a specialization filter for the profession - what happens when a player chooses not to select a specialization at all? Do I show all of the recipes? This introduces an edge case where 100% is not possible until a specialization is selected.

What happens when that player chooses a specialization or when they unlearn the specialization? Do those items magically disappear/reappear in the list?

While it doesn't suit the die hard "I only care about my main character" crowd, we feel that it's better for the ATT community if our stance remains as it is: For Recipes, multiple characters is the optimal and recommended way to finish your Recipe collection.

Here's one that will sting a bit:
Thistle Tea. There's a non-class bound version of this recipe that sells for gold cap. It can be learned for a few silver by a Rogue. It teaches the same exact recipeID as the non-class bound version. Would you rather spend 9 million gold or complete Cooking by simply having a Rogue?

I will counterargument your examples.

What happens when a player chooses not to select a profession at all? Well, I tested with a character without profession and there is no profession category. Other characters who have yet to learn some secondary profession and those professions are not in the profession category. The same with a character with only one main profession.

What happens when a character choose a profession and unlearn that profession? That profession disappears for the category because the character has unlearned it. If he learns later the same profession those recipes and the category appears again.

I think in both cases specializations should work like professions, maybe the empty category could be solved by showing an incomplete thing in professions with specializations that are only completed when the player learns one specialization. The same could be applied for characters with not every available profession learned.

About the Thistle Tea, I would not buy it for 9 million gold, but theoretically, it would be possible to learn all cooking recipes by my paladin even if in practice it won't ever happen but it does not change the truth that my paladin is missing that recipe. Multiple specialization recipes on the other are not possible, not matter how much gold and time I spend, is as impossible as having 3 main professions and yet in profession category, there are no more than 2 professions visible by any character.

Do not misunderstand me, I also have a goblin with Thistle Tea and a second engineer, but sometimes people could be interested in checking their account collection and sometimes in checking their character collection.

You solve this by having two Engineers. One with Goblin and one with Gnomish.

That only applies if account mode is active for recipes, not for character mode, after all you can also have every profession with multiple characters yet only the recipes of the professions for the current character are shown in the list.

Account Wide is the recommended setting for recipes as it is impossible otherwise to 100% the section on one character. Introducing mini filters for specializations over-complicates an otherwise simple solution.

I don't understand why do you think is impossible to 100% recipes in one character when is, in fact, possible by definition: Learn all the recipes for the profession and specialization of the character that has not been removed and is available for the faction, race, and class of the character.