dkw: It probably goes back to traditions like Strunk & White's "omit needless words," which I think is vague and unhelpful at best and detrimental at worst. Just because you
can technically omit something and still make sense doesn't mean you
should.
BlackBlade: Those sentences aren't technically ungrammatical, so I would say that it's just a stylistic issue. People frequently delete
that as a complementizer or relative pronoun, especially in speech, as in "He said he was going to the store." That's completely unambiguous and unobjectionable. When it becomes a problem, in my opinion, is when the next phrase or clause reads like a complement to the verb in the main clause, when it's actually part of a subordinate clause. They are what's called
garden path sentences, where the sentence is technically grammatical but very easy to misparse.