Hello Arthur,
I do not think that this would bring a lot of benefits, but would require significant efforts... because all dialogs should be reworked (also inner ones), buttons on the bottom of the dialog would already not fit in horizontal space and it would be necessary to place them on two rows (that I do not think is a good idea)... So I would prefer to not change the layout unless a lot of people would complain.
If space problem is bothering you, use Quick Search Bar - it can do the same as you have shown : marking of the all occurrences even easier then with Find dialog. And I would try to add more functionality to it (maybe 1.50) using a way suggested by Stefan (menu for search field as in Firefox or E-TextEditor).
Best regards,
Alex.