For all those people going "you shouldn't bathe kittens!" maybe you haven't had to take care of a kitten by hand before from 3 weeks of age. When our little Jimmy Six Toes was 3 weeks, he was a poop fountain.
I had to wipe his bum every few hours to get him to pee, but when he had to poop... it was terrible. And he was so little he'd just squirm and struggle against it, he was afraid of his own poop! Inevitably I'd have to bathe his hindquarters in a sink or he'd end up being covered in his own waste.
When you have to do *everything* for a kitten, including making them poop and pee... you do end up having to bathe them more often. If the kitten had a cat-mom, sure, he would not have needed baths. But, alas, he only had me.
(We also had to give him soap baths about once a week because he came to us covered in fleas, so it took about four weeks to get rid of them, the poor dear. We used mild dishwashing soap, of course.)
His skin is fine now and he's a super healthy rascal kitten at 5 months.