Digital watermarking techniques are crucial for copyright protection and source identification of images, especially in the era of generative AI models. However, many existing watermarking methods, particularly content-agnostic approaches that embed fixed patterns regardless of image content, are vulnerable to steganalysis attacks that can extract and remove the watermark with minimal perceptual distortion. In this work, we categorize watermarking algorithms into content-adaptive and content-agnostic classes and demonstrate how averaging a collection of watermarked images can reveal the underlying watermark pattern. We then leverage this extracted pattern for effective watermark removal under both graybox and practical blackbox settings, even when the collection contains multiple watermark patterns. For some algorithms like Tree-Ring watermarks, the extracted pattern can also forge convincing watermarks on clean images. Our quantitative and qualitative evaluations across eight watermarking methods highlight the threat posed by steganalysis to content-agnostic watermarks and the importance of designing watermarking techniques resilient to such analytical attacks. We propose security guidelines calling for using content-adaptive watermarking strategies and performing security evaluation against steganalysis. We also suggest multi-key assignments as potential mitigations against steganalysis vulnerabilities.