The reason for Mihawk to became Shichi Bukai was probably because he got bored of having to destroy weak Marines all the time
Remember Kuro was sick of always being attacked by the Marines in East Blue although he was stronger then them, maybe Mihawk and other Shichi bukai had this reason too
Also becoming a Shichi Bukai is the easy way to make a fortune you can kill others pirates take their treasures and still be considered an unwanted man that's a good way of life, no wonder BlackBeard wants to became a Shichi Bukai, that way he can attack all pirates he wants, get their treasures and still be free was a bird also he needs protection against WhiteBeard
WhiteBeard is a Great Pirate and also the strongest man alive in the World
Shanks is strong but probably at the same level was Mihawk the only diference is that Mihawk prefered to work for the W.G. and not be bored by Marines and Shanks went the other way
But those this make the Shichi Bukai weaker just because they work for the W.G. the answer is no
Because the Gorousei are probably the strongest men in the World after WhiteBeard and the reason they fear WhiteBeard and Shanks joining forces is because this would unbalance the situation making WhiteBeard even stronger
At least that's what I think for what I've seen so far