Why doesn't computer science follow biology more closely in computer design?
This might be more suitable as a comment than an answer. 

From computability point of view, any machine which uses finite memory (but not necessarily constant) at any point in time and modifies it according in a local way is equivalent to Turing machines (this is an informal statement of a result by Robin Gandy from 1980 IIRC). On the other hand Turing Machine models are simpler to deal with in many respects and therefore are easier as a object of study. Natural models of computation are usually more complicated to study.

There are also studies into natural models of computation. You may want to take a look at Aaron's answer here.