What you are discussing is called an elliptical clause (or an elliptical adjective clause, or an elliptical bound relative clause) whereby we drop the relative pronoun in an adjective clause where the pronoun is not essential to the meaning of the sentence.
To quote an online resource:
Elliptical Clauses are grammatically incomplete in the sense that they
are missing either the relative pronoun (dependent word) that normally
introduces such a clause or something from the predicate in the second
part of a comparison. The missing parts of the elliptical clause can
be guessed from the context and most readers are not aware that
anything is missing. In fact, elliptical clauses are regarded as both
useful and correct, even in formal prose, because they are often
elegant, efficient means of expression. (The omitted words are noted
in brackets below).
Coach Espinoza knew [that] this team would be the best [that] she had coached in recent years.
they were] sometimes nervous on the court, her recruits proved to be
Sometimes the veterans knew the recruits could play better than they [could play].
In regards to why it is appropriate, it is simply a matter of usage.
People dropped the relative pronoun for so long that omitting it became acceptable grammatical usage.
In other words, all of your sentences are correct, and you do not need to fret about one being superior to the other.
Have a nice day.