Wrong useage of the Word 'that'

I think there is probably no other word which is used wrong than the word 'that'.
The word 'that' is a pronoun, not a adverb.
You see it used in such ways as:
They saw (that) they were (etc).
How much more meaningful to say:
They saw they were (etc).
example:
When the time had come (that) they should (etc)
Much better to simply say:
When the time had come they should (etc).
My college English instructor called that kind
of useage "immature use of the word 'that'.
The word 'that', being a pronoun, should be
used only to point out a subject or person such
as:
See that flower?
That person is a (etc).
See over that hill?
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