A lot of comedy relies on the personality of the performer. Improv is rarely an exception. However improv is a discipline where the personality of the performer can actually get in the way.
In acting, certainly, the ideal is to lose oneself in the role. Become that character. However, that ideal is at odds with what the public seems to want. Many of the most popular actors tend to be people who keep the same character no matter what the role. Arnold Schwarzenegger, Sean Connery, Bruce Willis, Julia Roberts, etc. Most of the early Hollywood stars can be included as well. That's not to say they can't (or couldn't) act, but their success was in part due to a constancy in the characters they played.
Actors who lose themselves in a role tend to take a lot longer to get recognised by the public, basically because they are harder to recognise.
When the direct audience feedback of laughter is all that is sought by a player or a group, it is very easy to fall into bad habits. Joyful, well-rewarded bad habits, but habits that can make telling longer stories or playing scenes with any realism or honesty difficult.
So, in the same way that the perfect actor is one who loses him- or herself in a role, the perfect improviser is one who loses him- or herself in the scene. That is by being, saying and doing whatever the scene needs regardless of their regular habits, the things they like to do, their usual way of standing, moving and talking, and their standard set of stock characters. And often at the expense of the jokes that keep appearing in their head.
It seems like the path to getting singled out for praise less, but, if your fellow players all think the same, you will find yourself in a group that can play or do anything: tell fantastic stories, make awesome scenes and allow rich, nuanced characters to emerge that will stay with an audience long after the cheap fizz of a knowing block.