Agreed on several counts! My horse used to get all sorts of scratches (which would evolve to regular bouts of mild cellulitis), which more or less went to 0 when I started added copper and zinc (especially at opportune times of the year).
Plus, as you say - slather on some cheap zinc oxide (I got a big tub of the generic - slightly cheaper than desitin… which of course now I don’t use since the copper and zinc have worked so well). It softens the scabs perfectly, and acts as a gooey bandage to keep other grime off (which is key on pasterns during mud season). If you want to over-manage like I do, add a bit of triple antibiotic ointment (I wouldn’t add cortisone cream for this since I believe technically it can delay healing, but it’s a good triple threat for other skin irritations that are wanting to get inflammed/proud).