In my opinion, since Japanese is a head-final language and since the verb comes at the end of a clause, a sentence-final noun would be enough to indicate that the clause is a pre-modifier of the noun.
In English, the relative clause post-modifies its head noun and, even though a relative pronoun can be optional at times, there are certain clauses that require its use. For example, subordinate participial and subordinate passive clauses may be reduced. Relative pronouns are also optional in relative clauses in which the modified noun is coindexed with the object. The contiguous noun phrases could serve as an indicator of there being a relative clause, hence the optionality of the relative pronoun. However, subordinate clauses in the simple tenses require the use of a relative pronoun, if the noun being modified is coindexed with the subject of the relative clause, to explicitly indicate that what follows the noun is a post-modifying relative clause, not a simplex main clause in which the noun is the subject.
The cow (that is) eating the grass
The grass (that is) eaten by the cow
Clause where head noun is coindexed with object of RC
[The grass]1 (that) the cow eats ∅1
[The grass]1 (that) the cow ate ∅1
Clause where head noun is coindexed with subject of RC
[The cow]1 *(that) ∅1 eats the grass
[The cow]1 *(that) ∅1 ate the grass
The reason that subordinate clauses in the simple tenses where the head noun is coindexed with the subject of the relative clause require a relative pronoun is that without it, the head noun could potentially be parsed as being part of a simplex clause, not the head noun of a relative clause if the relative pronoun is omitted. Participial and passive clauses, regardless of coindexation, can be reduced due to the fact that native speakers intuitively know that there is no way a participial or passive clause can be a simplex clause without its auxiliary 'be', so there is no other alternative but to compute the clause as being a relative clause.
The grass eaten by the cow (never a simplex clause, so it must be a complex NP)
The cow eating the grass (never a simplex clause, so it must be a complex NP)
In Japanese, on the other hand, whether the head noun is coindexed with the subject or the object does not matter and there is no need for relative pronouns as there is no structural ambiguity whatsoever, since nouns never come after the verb in simplex clauses; when a noun does come after the verb, the clause preceding the noun is most certainly a relative clause.
牛 が ∅1 食べ-た 草1
ushi ga ∅1 tabe-ta kusa1
Cow NOM ∅1 eat-PAST grass1
The grass that the cow ate
∅1 草 を 食べ-た 牛1
∅1 kusa wo tabe-ta ushi1
∅1 Grass ACC eat-PAST cow1
The cow that ate the grass
This is, however, just my opinion. Whether there is any psycholinguistic evidence for such parsing complexities is not known by me.