The JR WEST ONLINE TRAIN RESERVATION website displays trains used based on certain conditions. If the selected area of the chosen train is not within an area that exclusively uses the Shinkansen, tickets may not be processed.
In that case, please search the selection again that exclusively uses the Shinkansen, or specify the train for each section by selecting "Do not change trains within an area".
(Example) When searching for "Hiroshima to Minami Fukuoka", selecting "Shinkansen (Use Hikari / Kodama)" will not allow you to book a ticket. Please search "Hiroshima to Hakata" again.