Plumtree, a former Junior All Black and highly regarded within the Hurricanes environment, joked Smith was too hard to replace.
"Those boots are way too big to fill and there's too much pressure," Plumtree laughed.
"At this stage of my life, I've still got three boys at home and I've got a big part to play in their lives as a Dad. I just want to be home and doing my thing with them.
"Right now it's important that I'm a good dad and a good coach for the Hurricanes.
"Being involved with the All Blacks is something I always wanted to do but family comes first for me right now, so I won't be applying for that job."
Welsh-born Rogers has been involved in two successful All Blacks' Rugby World Cup campaigns as Hansen's video analyst.
This year he became the Blues' defence coach after being hired by Tana Umaga.
"Alistair is at the forefront of development in a critically important part of the game at the highest level," Umaga said at the time."He is highly thought of by the All Blacks coaches and players alike and I'm absolutely thrilled he is coming to a full-time coaching position with us."
But Rogers said he wanted to concentrate on his current role with the Blues.