From politicians to podcast hosts, online platforms have systematically banned (``deplatformed'') influential users for breaking platform guidelines. Previous inquiries on the effectiveness of this intervention are inconclusive because 1) they consider only few deplatforming events; 2) they consider only overt engagement traces (e.g., likes and posts) but not passive engagement (e.g., views); 3) they do not consider all the potential places users impacted by the deplatforming event might migrate to. We address these limitations in a longitudinal, quasi-experimental study of 165 deplatforming events targeted at 101 influencers. We collect deplatforming events from Reddit posts and then manually curate the data, ensuring the correctness of a large dataset of deplatforming events. Then, we link these events to Google Trends and Wikipedia page views, platform-agnostic measures of online attention that capture the general public's interest in specific influencers. Through a difference-in-differences approach, we find that deplatforming reduces online attention toward influencers. After 12 months, we estimate that online attention toward deplatformed influencers is reduced by -63% (95% CI [-75%,-46%]) on Google and by -43% (95% CI [-57%,-24%]) on Wikipedia. Further, as we study over a hundred deplatforming events, we can analyze in which cases deplatforming is more or less impactful, revealing nuances about the intervention. Notably, we find that both permanent and temporary deplatforming reduce online attention toward influencers; Overall, this work contributes to the ongoing effort to map the effectiveness of content moderation interventions, driving platform governance away from speculation.