I would like to understand if there is deeper reason/motivation behind 
augmentations in homological algebra. Recall classically in homology
if there is a complex of free $R$-modules ($R commutative unitary ring)

$$ ... \xrightarrow{\partial_{n+1}} C_n \xrightarrow{\partial_{n}} C_{n-1}
\xrightarrow{\partial_{n-1}} ... \xrightarrow{\partial_{2}} C_1
\xrightarrow{\partial_{1}} C_0 \to 0  $$

then it can be turned to **augmented** chain complex by extending the right part
to
 

$$ ... \xrightarrow{\partial_{2}} C_1
\xrightarrow{\partial_{1}} C_0 \xrightarrow{\epsilon} R \to 0  $$

where $\epsilon(\sum_i a_i \sigma_i)):= \sum_i a_i \in R$


such that the $0$-th cohomology $H^0$ of the original complex and 
of the augmented complex $H^0_a$ are related by $H^0= H^0_a \oplus R$.

Fine, but the question is if there is any deeper philosophical reason 
behind using augmentations or is it just a historical leftover (I'm not sure who introduced this concept first. Eilenberg?) Moreover was it to pass to augmented objects just a "matter of taste" or was there some deeper mathematical reason behind? 

(Maybe it's in *certain sence* more flexible for certain generalization directions. For example to work in some situations more "uniformly", I don't know, that's just a guess) Obviously there is no information
gain/loss when passing to augmented objects. Are there nevertheless any advantages
to pass to them? For example does this concept maybe provide better 
structural /functorial compatibilities or say "more natural framework" when working in more general setting (eg simplicial objects in higher categoy theory)?