I feel like you didn’t think about this before you commented. Fritz the crown prince obviously has feelings for the duke, he just wanted an excuse to see him in person.
Firstly I thought like you but Fritz was always sending flowers which emphasized his intentions and duke realized prince's feelings so Prince actually didn't need an excuse for visiting his best friend and unrequited love. It might be weak example but also there is other issues with, my favorite character, the other duke. He easily kidnapped and threated another duke yet we might say that it could be but he can't dare such a bold move that would cause a diplomatic crisis if we consider his relationship with his father. His action doesn't suit his character structure. I might make excessive reading but there are some parts which completely fit the plot. However you might be right, it can be just an excuse ╮(￣▽￣)╭
Plot is full of nonsensical parts ┑(￣Д ￣)┍ Prince of all empire goes to some duke's house just to deliver duke's order of clothes! Are you real?(￣∇￣") he is a member of fucking monarchy! He is not an ordinary neighborΣ( ￣□￣||)