To investigate the impact of full-touch screen infotainment system response speed on car-following safety, this paper conducts human-machine interaction experiments using real car-following videos in an in-vehicle cockpit simulator. Data are collected from 25 participants under 2 vehicle speeds and 3 response speed conditions during both static and dynamic car-following scenarios. The visual distraction data are analyzed to reveal correlations between system response speed and car-following safety risks. Results demonstrate that as response time increases from 0 to 800 ms, the Total Time Spent on Screen (TTS), Glance-to-Screen Count (GSC), and Single Operation Time (SOT) exhibit nonlinear gradually growth with decelerating rates. Specifically, at 80 km/h, when response time increases from 0 to 400 ms, the TTS, GSC, and SOT increase by 17.83%, 19.74%, and 28.72% respectively, while the smaller increments of 10.97%, 12.89%, and 18.06%. When preceding vehicles braked at a 3 s time headway, the minimum following distance decreases by 14.5 m (80 km/h) and 12.78 m (100 km/h) as response time extends from 0 to 800 ms. Simulation results across 3 time headway levels confirm that slower system response significantly increases both collision probability and severity. These findings provide theoretical foundations for designing safer full-touch HMI systems, highlighting the critical role of optimizing response speed in mitigating driving risks.