There are occasionally wounds I want to dry out. For example, one of my horses superficially grabbed her quarter running around like an idiot the other night. The pasture is a mud pit; there’s no way to turn her out and keep it clean, not even with a wrap or boot. So in this particular instance, I want it to dry and toughen up quickly to help protect it from the elements, because the only other option is stalling her for an otherwise minor abrasion.
But for most everything else, once they dry up, I find it a) takes slightly longer for the hair to grow back and b) increases the risk of scarring.
Nothing should be “oozing” with good wound hygiene, not even in the dirtiest of environments. If it’s a major wound, you will have drainage, but “oozing” on superficial scrapes means you have allowed a secondary infection to become established. Good wound hygiene involves daily cleaning until the wound has closed from the inside, regardless of the topical applied. I use wet 4x4s with a small amount of antimicrobial scrub, like chlorohexidine.