Although beneficial information abounds on social media, the dissemination of harmful information such as so-called ``fake news'' has become a serious issue. Therefore, many researchers have devoted considerable effort to limiting the diffusion of harmful information. A promising approach to limiting diffusion of such information is link deletion methods in social networks. Link deletion methods have been shown to be effective in reducing the size of information diffusion cascades generated by synthetic models on a given social network. In this study, we evaluate the effectiveness of link deletion methods by using actual logs of retweet cascades, rather than by using synthetic diffusion models. Our results show that even after deleting 10\%--50\% of links from a social network, the size of cascades after link deletion is estimated to be only 50\% the original size under the optimistic estimation, which suggests that the effectiveness of the link deletion strategy for suppressing information diffusion is limited. Moreover, our results also show that there is a considerable number of cascades with many seed users, which renders link deletion methods inefficient.