Our would-be clean-speaking friend was dismayed to then be told by his coworker that all that didn’t cut the mustard either; the in all that had to go. So, describing himself as a reasonable fellow…. all for improving myself, he asked for our advice.

Our advice is this: don’t worry about all that. It’s true that removing the from the phrase all that often doesn’t change the meaning of a message much at all. Just think of the Armed Forces slogan: Be all that you can be. Sometimes, that that adds a desirable emphasis.
It is also true that using that after the pronoun all is quite well-established and perfectly acceptable. Alfred Lord Tennyson used it just that way when he wrote, But teach high thought, and amiable words/…And love of truth, and all that makes a man.