I understand the value of focusing on only the part of something to try and understand it better. It’s an essential part of the way we make sense of our world. BUT we must never lose sight of the fact that we CANNOT understand the whole by understanding the parts when we deal with complex adaptive systems.
My own area of medical practice is holistic and that’s not a New Age concept – it’s a focus on the person, rather than just a part of the person which is damaged (the pathological lesion).
A couple of authors I’ve read recently have used other vocabularies to address this issue. Robert Solomon describes a focus on parts as “thin” – it lacks “richness” and “depth”. That strikes me as very true. There’s too much left out of explanatory models which are reductionist. So much left out in fact that they fail to help us understand real life complexity. And Andy Clark uses the term “componential explanation”. Somehow this immediately makes sense to me. He shows how this only works when “the parts display the relevant behaviour even in isolation from each other.” Otherwise, we try a “connectionist explanation” similar to that described so beautifully by Barabasi in Linked. But, he points out, even a focus on the connections is not enough and he describes another model – “emergent explanation” (as explored in Dynamical Systems Theory). This is a good explanatory model for real life complexity and includes a study of “collective variables, control parameters, attractors, bifurcation points and phase portraits”.
Now doesn’t that sound much richer than the reductionist approach?
Heroes Not Zombies 
I coudln’t agree with you more. As a huge proponent of homeopathy I see the benefit of the wholistic approach. A gear is a gear. Keep it away from water, salt, and other rusting agents the the gear will be fine. But a collection of gears is a complex machine with a purpose . . . a goal. To retify an issue, the answer may be found in a gear that doesn’t even have the problem. But beware that you don’t forget the purpose of the machine. Too many gadgets exist that should work in theory . . . but they only work in theory. This is because too much emphasis was on asthetics and not on mechanics.
Most systems are far too complex to be reduced to the lowest common denominator.