Step 1: Clarification of the Inquiry:
The query requires identification of the foundational Sanskrit grammatical work that explicitly details the objectives and merits (\textit{prayojana}) of grammar study (Vyākaraṇa).
Step 2: Detailed Exposition:
While all provided texts are significant in Sanskrit linguistics, Patañjali's Mahābhāṣya is most renowned for its systematic articulation of grammar's advantages.
The Mahābhāṣya is a commentary on Pāṇini's Aṣṭādhyāyī. Its initial section, the Paspaśāhnika (introductory chapter), is dedicated to this subject. Patañjali outlines key benefits, including the preservation of the Vedas (\textit{rakṣā}), appropriate modification in rituals (\textit{ūha}), comprehension of tradition (\textit{āgama}), conciseness (\textit{laghu}), and resolution of doubt (\textit{asandeha}).
Aṣṭādhyāyī: Constitutes the primary rule compilation; it does not discuss grammatical benefits.
Nirukta: Centers on word origin and categorization.
Vākyapadīya: A profound philosophical discourse on language, words, and meaning; however, the canonical enumeration of practical advantages resides in the Mahābhāṣya.
Step 3: Conclusive Determination:
Patañjali's Mahābhāṣya is the text that comprehensively elaborates on the advantages of grammatical study. Consequently, option (2) is the correct selection.