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 use this concept just a matter of "taste" or was there some deeper mathematical reason behind?

(Maybe it's appeared 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 dealing in more general setting (eg simplicial objects in higher categoy theory)?