"They" isn't really used illogically.
If someone wants to understand, they only need to examine it beyond what they learned as rules in English class.
The use of "they" is usually general, when not really pointing to a specific person. If Dennis is standing in front of me, and someone asked me whom to speak to, I wouldn't point at Dennis and say, "They is the one to speak to".
But if I was talking about DennisP online, and I didn't know who was behind that vague identifier, and someone asked whom could help, I might say, "I talked to DennisP earlier, and they helped me with my problem."
For all I know, "DennisP" is an organization, or shared account. It's a vague generality, when the individual attributes of a person are unknown or irrelevant.
It's like when one speaks in general ways that apply to all mankind, and you might even use the word "you" to refer to, not YOU, but anyone.
"They" works great because a group is a vague fuzzy kind of thing. In the plural form, speaking of them, over there, and their attributes, it's not so much about the plurality, as it is the abstract fuzziness of it.
All that we're doing is applying that same fuzziness in the direction of what could possibly be a smaller target in terms of numeration.
That is why, I don't think those rules about singular and plural were ever really correct. It isn't the numbers that we were trying to convey with the words, but the fuzziness.
"He" and "She" are referencing specific object types with common properties across the whole of the specific object. Whereas "They" is referencing an object with either mixed or unknown properties.
Do you see what I'm saying? It isn't about the count, but the uniqueness of known attributes for a specific target. It just so happens that when you have many of an object, the commonality of attributes blurs, and so the "they" pointer appears to be about the number of objects. Then some people who aren't thinking beyond that get upset if you violate the number when using they to point to >1.
When really, it's just about fuzz.
I don't use "they" as any kind of feminist thing. I just think that "he or she" is not only incredibly distracting and inefficient, but it is the illogical one. Also referring to fuzzy things as "he" or "she" are both wrong, because they are trying to instantiate objects using a template that requires certain attributes when the properties of the spoken of object are unknown or irrelevant to the conveyed concept.
"He" when the boy template is needed. "She" when the girl template is needed. "They" when a fuzzy generic container works better. The number of people references is irrelevant. Just like how an organization may contain many people, but we refer to it as if it were a person. Even an individual person is an organization of smaller components.