WordPress tables are a double-edged sword, in spite of WordPress' progress over the years. They are the perfect candidates to present data, but unfavorable to tell a story. If you think that's not bad enough, wait until you hear about smartphones and tablets: devices where you have even less space to display data. There are some table disadvantages you have to learn to live with, but responsiveness is not one of them.
The last major update to WP Table Manager introduced a new responsive design for tables with additional responsive options. Now, there's a newer and better version of the WordPress table manager that adds a new responsive mode and new options to help you customize responsive tables and their behavior: repeated headers.