Command-F should ALWAYS focus into the Search panel...

I 100% agree. Ctrl-F should toggle Search open and place the cursor in the 'Find' field. On every instance, even if it's redundant. Like nearly every other application on earth. I have lost count of the times I've hit it while the pane is opened, then typed garbage into the document itself.

The alternate commands avoid closing the pane and dumping the content into the document, but are still... misdirected.

https://indesign.uservoice.com/

This is best place for feature requests

In the Edit>Keyboard Shortcuts you can define these and change them to CMD or CTRL F

Product area : Text and Tables

Load Find and Find Next instance --- Text: Shift+F1
Load Find with selected text --- Text: Ctrl+F1
Load Replace with selected text --- Text: Ctrl+F2

This will not close the Find dialog box

There are also similar shortcuts for the GREP etc.

You can define  your own shortcuts that suit you.

Click - Show Set to display text file of the shortcuts so you find them easily