Thinking like this is awesome when it happens: a lab I worked in would combine structures of motor proteins with single molecule studies, targeted mutation work, and even in-vivo studies. The result? You could take specific loops and helices within the motor and not only understand where and how they interact with a microtubule, but also how that affected the motor's mechanical action and cellular behavior.
Another real problem is we don't teach students anything anymore on the premise that there's too much to know, and as long as you can look it up, it will be fine. Or if you are working interdisciplinarily, your colleague will be able to tell you (of course they're relying on you too so there's a bootstrapping problem). This is terrible. Sometimes you need to call someone on their bullshit, say during a lecture, or even more importantly during a meeting where actionable decisions are being made and critical insight can avoid wasting time and effort. If you don't have a significant depth of knowledge, which multidisciplinarity typically doesn't encourage - because it's hard - you are just a body making warmth in that room. You need to have instant recall of as much related information as possible at all times when doing science.
This is spot-on correct. In the lab I worked in, we are working on a gene cluster of 11 genes, that result in the assembly of an enzyme that creates hydrogen. The PI's project was to play around with "promoters" that tell the bacterium to produce the genes. Think of this as 'script kiddie' work. I came in and immediately told him that this was the wrong approach; we had to alter the structure and chemistry of the enzymes themselves (think of this as 'assembler-level hacking'). Thankfully he was sympathetic to my argument and let me play around; I achieved a 3x improvement in enzyme activity. This summer,we tested the original idea, and all of the variants we tested were worse than what we started out.
Also, and this is my highly opinionated position informed by my experience as the sole chemist in a synthetic biology lab, but part of the problem is that a lot of biologists tracked themselves into biology because they didn't do so hot at chemistry. Many synthetic biology problems are chemistry problems, and even problems that are not on first blush like those that Drew Endy are trying to solve really become easy to grok if you're used to thinking qualitatively in terms of statistical thermodynamics and can mentally estimate collisions per nanosecond, from concentrations and kinetic parameters. These are quintessentially chemistry skills.
reference: https://www.ncbi.nlm.nih.gov/pubmed/23819621