I think "that" can be as important as any conjunction or preposition; if I have some residue of my basic grammer. If the sentence is confusing without "that," then it is too important to put it into the virtual wheelie bin.
Other writing defects get up my nose. One is using "say" or "said" with Every speaker tag, and even disjointing the speaker tag from what was spoken. The tag and the quote go into the same and one paragraph; unless it is a long-winded speech... Some tags could use "ask," "test," "complain," or any other descriptions of the nature or how it was to be said. In fact, I rarely use "say" and "said" and maybe should because it was merely said, but am apt to use "state" or "stated."
Second is my campaign. Starting sentences with "there" seem to be poorly writ. When I find that I have done so, a rewrite always seem better. I know it fall into speech, so I tolerate my characters starting sentences and paragraphs with; "there once was a young lady banker, who slept while her ship lay at anchor...."
"The avalanche has started. It is too late for the pebbles to vote." -Ambassador Kosh Naranek
