Incomplete Multi-view Clustering (IMC) has emerged as a significant challenge in multi-view learning. A predominant line for IMC is data imputation; however, indiscriminate imputation can result in unreliable content. Recently, researchers have proposed selective imputation methods that use a post-imputation assessment strategy: (1) impute all or some missing values, and (2) evaluate their quality through clustering tasks. We observe that this strategy incurs substantial computational complexity and is heavily dependent on the performance of the clustering model. To address these challenges, we first introduce the concept of pre-imputation assessment. We propose an Implicit Informativeness-based Selective Imputation (SI$^3$) method for incomplete multi-view clustering, which explicitly addresses the trade-off between imputation utility and imputation risk. SI$^3$ evaluates the imputation-relevant informativeness of each missing position in a training-free manner, and selectively imputes data only when sufficient informative support is available. Under a multi-view generative assumption, SI$^3$ further integrates selective imputation into a variational inference framework, enabling uncertainty-aware imputation at the latent distribution level and robust multi-view fusion. Compared with existing selective imputation strategies, SI$^3$ is lightweight, data-driven, and model-agnostic, and can be seamlessly incorporated into existing incomplete multi-view clustering frameworks as a plug-in strategy. Extensive experiments on multiple benchmark datasets demonstrate that SI$^3$ consistently outperforms both imputation-based and imputation-free methods, particularly under challenging unbalanced missing scenarios.