Back when I was still a PhD student, I randomly walked into a career fair booth at a conference, where a department head (from a university that I don't now remember) sat at table and gave "mock" interviews/advice to candidates like me. I, on the other hand, was completely "green", without a clue for what it means or takes to become faculty. All I knew was that I was doing exciting work, publishing well, my professors liked me, and I wanted to continue in academia. So, as soon as my turn came to sit across the table from him, words began pouring out of my mouth about my PhD project:
-"I did THIS, and I did THAT! Got these AMAZING results!!", I said.
When, suddenly, he cut me off, and abruptly said: "You are in the wrong mind-set: you started by telling me by what you DID (the past), while as a professor you should be telling me about what you are GOING TO DO (the future)".
The reason why I bring up this story, is because I just witnessed a highly-qualified postdoc, who I am sure is brilliant in what he does, crash-and-burn during his on-site interview (most likely, without even realizing it!!). The problem is that it is a natural human tendency to continue doing what you are best at. So, when this person gave his chalk-talk, he essentially proposed extending his postdoctoral projects further. The whole presentation felt like a PhD student reporting to his committee during a defense, and that just NOT cut it.
You must understand that a professor in the US is effectively a "CEO" of a small start-up "company". So to be a successful CEO, one must have: the people skills to manage personnel, the know-how to navigate the murky waters of academic bureaucracy, the understanding of the funding landscape, the
perseverance to get up when someone knocks you down hard and continue pushing your idea against all odds, the "silver-tongue" to give your 5 minute elevator pitch and attract "angel" funding (ie, talking to program officers), the spark to "infect" others with the enthusiasm for your work (convince grant reviewers to recommend you for funding), the time-management skills to do all of the above... oh-and-by-the-way, teach/publish/serve on committees/present at conferences/do science and have a life while at it... and the list goes on and on.
So put yourself into the shoes of the hiring committee: if you had to "bet the farm" on just one candidate (out of 100 very qualified people knocking on your door) that he/she will be successful in everything I just described above, how would you choose that person who will be entrusted with ~million of your money? How would you choose that visionary - the next mini-Bill Gates or Mark Zuckerberg? What quality would you look for in these people? The answer is "Independence".
It is simply, not enough to be a good "grunt" (postdoc/student/technician). You can be the most gifted scientist, with a stellar publishing record and a polished resume, but if you fail to project that you have a (YOUR OWN) "vision" and you can see "the big picture" (how to fund your ideas, who to collaborate with, what your strengths and weaknesses are, what equipment you need, etc). My heart pains pains for you, but there is nothing that I can do to sway the search committees' decision in the other direction. The opportunity is only yours to lose...
Same goes for writing proposals. If you say that you are going to continue working with your previous PhD or postdoc bosses, you WILL get shut down. It is almost like an eagle pushing out its babies out of the nest, so that they can learn how to fly. Its painful, but it must be done. So, my advice is: seek independence, and you will be successful!