Could physically simulating neural structure on a fundamental level yield superior results to machine learning algorithms?
Very interesting question. Although I have not a single little bit of expertise in this area, I do have some references you may want to read. First is a paper by Merz and Fromherz (2005) where they grew snail neurons on a silicon chip. Pfister et al (2007) also tried to grow neurons to allow interfacing between neurons and machine (for neural prosthesis e.g.). There is thus definitely a field of research that believe neural interfacing may be better than mechanical and algorithmic networks.  

There has been 10 years worth of research since these papers so I bet there are some advancements that may give you a more definitive answer than mine.