Push notifications remain among the most direct channels through which digital platforms engage users, yet existing approaches have invested heavily in who to notify, when to notify, and what to recommend, while leaving how to communicate as the least-optimized stage. This paper argues that message quality is an independent, underinvested lever, and that LLMs create their most differentiated value precisely at this layer. We make three contributions. First, we define notification message quality along six dimensions (contextual relevance, clarity, actionability, novelty handling, linguistic freshness, and persuasive appropriateness) and show how LLM-based composition improves each relative to templates. Across reviewed deployments, reported improvements range from +8% to +14.5% CTR over static templates and +1% to +2.5% over mature slot-filling systems, though these span heterogeneous systems and should not be treated as directly comparable. Second, we provide an architectural attribution analysis disentangling message generation from adjacent components (targeting, ranking, timing), arguing that observed gains are frequently misattributed to text generation alone. Third, we introduce a three-criterion decision framework specifying when LLM generation is and is not the binding constraint. We support these arguments through a PRISMA-guided survey (28 sources from 142 screened), examine domain-specific applications across social media, food delivery, and e-commerce, and propose a unified architectural framework with budget-aware routing, grounded generation, candidate ranking, diversity controls, and online learning.