Medicine Cats

Why are medicine cats not allowed to take mates or have kits?  It's not part of the Warrior Code, yet it is still a rule, and breaking this rule results in severe punishments, either by StarClan, the cat's Clan, or other cats.  The basis for the rule is that a medicine cat's duty is to the Clan as a whole, and a mate and/or kits would interfere with that.  However, medicine cats can still love other cats, probably because that is unavoidable, and that itself interferes with their duties as a medicine cat.  If Spottedleaf or Cinderpelt was faced with the decision to try to save Firestar from a fatal wound or to try to save a young warrior from a possibly fatal wound, they would still devote more attention and energy to Firestar, even though his wound was fatal, because they loved him.  This would also happen if a medicine cat was very close to a sibling, their mother, their father, a niece, a friend, etc.  The medicine cat may not even realize it, but they will devote more attention and energy to a cat they loved than to a cat that was just a member of their Clan, regardless of if the medicine cat had a mate and/or kits.  This means that the reason behind the rule has no foundation.
The rule also only applies to kits born after a cat has become a medicine cat.  Mudfur became a medicine cat after he had already taken a mate and had kits with her.  While his mate and three of his kits had died before he became a medicine cat, Leopardstar, his surviving kit, did not die until long after Mudfur.  If the rule exists so a medicine cat is devoted to their Clan and not their family, why was Mudfur allowed to become a medicine cat?  Not only did he break the rule, he was openly allowed to by his Clan and StarClan, and he suffered no punishment for it.  I don't see how this situation is truly any different than a medicine cat having a kit after the cat became a medicine cat.
The next argument might be that carrying kits would interfere with a female medicine cat's physical ability to take care of their Clanmates.  However, Yellowfang and Leafpool both carried kits while they were medicine cats, and it did not interfere with their abilities.  They continued to perform their duties so well that they were able to hide the kits they were carrying, when Clanmates can usually easily recognize that a she-cat is carrying kits.
With all that in mind, what reason is left for why a medicine cat is not allowed to take a mate or have kits?  I certainly can't find one.