English has Rules, Just Like Japanese!

[MaraD_]

And how would that work with the examples given in the Wikipedia article I linked earlier?
Could you write those sentences with "it"? Would that seem appropriate? Would it be better English?
It might be grammatically correct, but it's not the normal word you use in that situation.
There's nothing new or remarkable about using "they". You probably don't even notice it in most contexts.

"Seem" is almost subjective in this case, due to what Ive said prior.
Obviously it seems wrong (though partly because it wasnt done correctly) but none the less, their, they, them are proper plural versions of it.
Theys, thems, and theirs, should be incorrect, just as "its" should be incorrect.
(Not possessive, but plural neutrals.)
also, im going to adjust what you wrote a tiny bit. (the last 2 were fine, but ironically should have been plural in patient/journalist)

"It left its umbrella in the office. Would it please collect it?"

or

"Someone left ones umbrella in the office. Would one (or that person) please collect it?"

("He" would have been gender neutral in the past and fit rather well too, before it was corrupted to mean adult male. But this only applies if the person is limited to the adult age.)

"The patient should be told at the outset how much one will be required to pay."

"The patients should be told at the outset how much they will be required to pay."

-

"But a journalist should not be forced to reveal ones sources."

"But journalists should not be forced to reveal their sources."

Back to the point, inserting "it" sounds wrong to us, because we've made it wrong.
But this never should have been the case. We ascribed the word "it" to mean objects/animals, because we assume we werent animals (we are) and because we didnt see nongendered people in the past. Even more so when we were far more focused on gendered roles back then.
So how could there be a situation where a person doesnt have a gender? Only when a situation had an unknown person, or will have an unknown person. but again, due to gender roles, this also limited the number of people that could meet the requirements, usually by gender.
example: "Once the position is filled for the job "the person" will be required to this list of activities."
the job was already long since decided which gender was going to be doing the tasks.

but in the case of something like theft, the perpetrator could be referenced genderless, if it was a crime that was considered to be common among both genders.
The word "it" would be used so rarely, it would come off as jarring. (along with how people didnt want to be associated with animals.)
The dog went and got "its" bone.
The dog can be male or female. Sometimes the gender is known, and it still works fine.

They/Them/Their applies to the only situation in which humans can be multiple genders, when in a group.
So no one batted an eye when the use of they, them, their started being used for people.
And it grew in use for singular pronouns.
But it was slang, and eventually considered normal use of the word.