A famous writer (I forgot who or where) once complained about not being able to avoid 'the fact that' in his writing. Such inelegance! Yet he just couldn't bring himself to remove it from every sentence—which he could have done, because reducing 'the fact that' to a plain 'that' always results in a grammatically correct sentence. In fact, I once worked with a copy editor who did just that: She returned my manuscript with every instance of 'the fact that' reduced to 'that'. In all cases, the result was grammatically correct. But in some cases, the result was also atrocious.
So why do some sentences just seem to require a 'the fact that', even when it is grammatically redundant and almost universally despised? I have given this matter a disproportionate amount of thought, and arrived at the conclusion that it is all about expectations.
The word 'that' can have several grammatical roles. It can be an adjective, as in: 'that capybara'. (Which capybara? That one!) Or it can be a conjunction, which is a word that introduces a subclause, as in: 'Do you know that capybaras are the largest rodents?' ('That' can also be a pronoun, of course, but let's forget about that for now.)
Now here's the thing: You often don't know which role 'that' has until you've read the entire sentence. And that's confusing. For example, after reading 'I like that …', you still don't know whether 'that' will be an adjective ('I like that capybara') or a …