Making Favorites category selected by default in Character Viewer
It seems that it has been a while since you have asked this question but I still wanted to respond to it because it had gone unanswered and you or somebody else might still use a solution, even if not perfect, to the problem you described. 

I have the same problem with the Character Viewer on my iMac running on High Sierra. 

The most practical solution I could find was opening it using the keyboard shortcut ⌃+⌘+space and always leaving / closing the Character Viewer when it is in the compact / pop-up state (see the picture). This helps because, if invoked through its keyboard shortcut, the Character Viewer always opens in the state it was in when it was last closed and focuses on the last used category such as the Favorites. You can click on the icon at the Character Viewer's top right to switch between its compact and expanded states.

If I do the above, the Character Viewer always opens in the compact state and focused on the category I left it with. Because most of the characters I use are in my favorites, it nearly always opens focused on the Favorites or the Frequently Used &amp; the Favorites. Interestingly, I don't have this problem with the Character Viewer on my MacBook running on Catalina. It opens focused on the category wherever I left it in including the expanded state.