The reality of a self-defense situation is that the hands will not be protected by wraps & over padded gloves when it makes contact with the hard bone of a human skull or face. This is going to lead to an injured hand and possibly the loss of that particular fight.
The popularity of boxing, kickboxing and other combat sports for fitness has diluted some of the most important facts about the use of these techniques during a live self defense situation when health and life are at true risk. Well one thing that any true combatant of the streets knows it that one of the most important things to be attentive about when combating for real, is to assure that your knuckles are conditioned to hit bricks, and that the execution of your strike better be precise and straight or you will take yourself out of the fight.
I do agree and even teach my students to use the palms and fatty part of the hands to strike during a real combat situation when hands are not wrapped or gloved. Old school techniques such as Palm Strikes, Hammer Fists, Ear Claps, Eye Flicks etc... can help to avoid hand injury and actually can be more effective than punches can.
Punches during real combat are not as effective as we all have learned to believe they are through watching movies and slugging boxers whose fists are blanketed in gobs of padding & tape. The execution of a proper, non self injuring punch even with gloves on takes years of dedicated training to master for use in combat. Bag gloves and padded bags play a big role in the widely accepted illusion of masses of people who believe they can use their punches expertly for self-defense, even though they have never even punched a padded training bag without wearing protective gloves.
If you practice punching for fitness, fun or competition, you are conditioning yourself to punch and you most likely will punch during a stressed moment or self-defense situation. This will not be good if you are not training to fight bareknuckle. You most likely will injure your hand even if you win the battle. However, I would not suggest that you stop your Boxing training. It is good for you. I suggest that you add bareknuckle training to your regimen.