Everybody wants to be heard. I would think that the desire to be heard is probably the most common reason why people engage in dramatic behaviors. They can get really loud, very intense and most certainly pretty visible. Most likely their drama is about a topic that has nothing at all to do with their innermost feeling of wanting to be heard/seen, yet the dramatic behaviors do draw attention and fulfill this desire, albeit only partially, as the actual reason for wanting to be heard may lie somewhere else.
I see drama as a pretty desperate way of getting attention. Upon musing why drama exists, I would like to come clean. I've lived in this life with a strong predisposition for drama, stemming from my personality. I've worked very hard at overcoming the need to express myself dramatically, especially in a negative manner. The gift of this work lies not in being entirely drama free - I am admittedly not! The gift lies in having intimate knowledge of the feelings around the need for drama, it's workings and the draw that exists when drama calls. I do not only hold this knowledge, I have immense compassion for anyone who sits in a place, in a body with a personality where drama is prevalent. It's not an easy road. However, it's a road that has many gifts hidden along the way, once a drama queen (king) embarks on it with the sincere desire to seek a way out of the compulsive need to "do drama".
To a dramatic person, drama isn't feeling very dramatic - it's just their "feelings". Truth is, it isn't their real feelings at all. The drama is a way to actually hide deeper emotions that would be difficult to deal with. The way I have experienced drama is that it is similar to anger or violence, in a sense, it's used as a cover up of feelings of vulnerability, low self-esteem or similar imbalances.
One way out of drama, into the place of authenticity and balance is to first recognize and fully embrace the facts of "Yes, I am doing drama - on and off, or even during greater bits of my time here on Earth. Once this "admission" of the facts has been accepted, the next step would be to focus on gratitude. There are countless things a person can feel grateful for. I like to be thankful for little things, before embarking on the tougher ones like "I'm grateful for my life in this body". Gratitude is an emotion that can be conjured easily (I'm grateful to see flowers emerge again and show me that it is Spring time" for example) and it carries a very soothing, healing sort of energy that can bring in higher vibrations and connect an individual with their true essence, which is unconditional love.
This focus on gratitude is a simple tool, quite undramatic really (not that appealing to dramatic people), but drama is a strong force, so this tool needs to be applied regularly and for a prolonged amount of time in order to bring a different life experience and thus slowly allow a different perspective which in turn will, once it sets in more fully, bring about a different reality. To overcome the need for drama does not mean that a person will completely be free of the "talent" for drama, but perhaps this talent can then find a more suitable expression, perhaps in the areas of art, instead of running rampant, ruining relationships, making reasonable communication near impossible and never filling the heart with the one thing a dramatic person truly wants - the feeling of being heard (seen) and loved for who they truly are.