The highest frequency city pairs I can think of, at peak periods, looking at available tickets this week:

Shanghai Hongqiao to Hangzhou East is about 10 high speed trains per hour, all trains using the same line.

Tokyo to Shin-Osaka is also about 10 high speed trains per hour.

Taipei to Taichung is 8-9 trains per hour, high speed + conventional. Shanghai to Suzhou is similar.

Rome to Florence is 6-7 trains per hour.

Hong Kong West Kowloon to Shenzhen North is 6 high speed trains per hour.

Beijing South to Tianjin is 5-6 high speed trains per hour.