A recent study published on arXiv highlights the increasing interest in variance-dependent regret bounds within the contextual bandits framework, with a particular focus on Thompson sampling algorithms. While much of the existing research has concentrated on upper confidence bound (UCB) methods, this paper draws attention to the limitations of current Thompson sampling approaches. Specifically, it critiques LinVDTS, an existing algorithm that is restricted to linear reward functions and exhibits suboptimal regret bounds. This limitation suggests that LinVDTS may not be broadly applicable across more complex or nonlinear reward scenarios. The study underscores the need for variance-aware methods that can extend beyond these constraints to improve performance in contextual bandit problems. By addressing these gaps, future research could enhance the applicability and efficiency of Thompson sampling algorithms. This focus aligns with a broader trend in machine learning research aiming to refine regret bounds by incorporating variance considerations.