my great dane with natural floppy ears never had a single ear infection or "stinky" problem and didn't need to be cleaned any more often than a dog with natural prick ears, same with all of my other floppy-eared dogs. Ear infections are more often a sign of a food allergy, nothing to do with whether the ears stand up or hang down.
There is absolutely NO reason to crop a dog's ears nowadays except for cosmetic purposes, and it's a horribly painful thing for a puppy to go through, even if it's done by a vet. And after the procedure the poor puppy spends its formative months hindered by sore, taped-up ears. It's horrible and should be banned on animal abuse grounds here like it is in much of the world. If you want to own a dog whose ears stand up, please use breeding to select for dogs whose ears stand up, not surgery.
Pit bull crops- where the ear is basically hacked off close to the head- are traditionally supposed to be done at age 2-3 days, the same age as when tails are docked. I don't think the puppy feels much at this age, or at least the tail-dock proponents claim they don't. Cropping the ears in a fighting pit bull does have a purpose- keeps the ears from being ripped up during a fight. It's possible many "breeders" of these dogs just routinely chop the ears off all of their puppies in hopes it makes them more marketable.