with 复合结构中 having done 和 done 的疑惑

By all reports, Bridge Climb is fantastic and one of the“must dos” while on a trip to Sydney, with royals and celebrities such as Prince Frederik and Princess Mary of Denmark, Matt Damon,Hugo Weaving,SarahFerguson,Cathy Freeman and Kostyra Tszyu all having done the climb. 

这里面的 having done ，现在分词完成式，是强调已经完成，那为什么不可以是done，过去分词呢？ 而且 having done 是强调分词的动作先于主句谓语动作，这里面是with复合结构，是不是没有这层含义，只有主动的意义？