Learn English – “You will be informed of this by email” – or is it “informed of that”

pronouns

From a lang-8 post:

Once the necessary documents have been received, your account will be activated and you will be informed of that by email.

I've recommented to change the pronoun that to this. But why exactly? This signals greater proximity relative to that, and sometimes emotional proximity, according to this answer.

Is the 'emotional distancing' conveyed by that the main obstacle? Or is it also technically wrong to use that in "you will be informed of __ by email"? Are there instances where we can use that in this phrase and be sure that it sounds natural?

Best Answer

Captain, where are we going on this mission?
-- You will be told of that when the time comes.

Dear Mrs Smith,
I regret to inform you that your husband, John, won't be coming home. He was sent on a dangerous mission to one of the moons of Jupiter, and his rocket ship has malfunctioned and cannot take off again. There will be no rescue mission. He was informed of this before he left but decided to go on the mission anyway.
Sincerely,
Buck Rogers

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