Here are some scattered thoughts: I'm not sure if they really answer what you seem to be driving at.

Complex analysis still gives you examples with nasty maximal ideal spaces, e.g. $H^\infty(\Omega)$. Even when $\Omega$ is the open unit disc, the spectrum is non-metrizable and not at all straightforward to understand (there ought to be some discussion in Gamelin's book).

$L^\infty$ has non-metrizable spectrum, although its structure is in some sense not as mysterious as that of $H^\infty$.

Note that every Banach space $E$ embeds as a closed, complemented subspace of a uniform algebra. Namely, take the canonical map from $E$ into $C(B)$, where $B$ is the closed unit ball of $E^*$ equipped with the weak$*$-topology, and let A be the closed subalgebra generated by the image of $E$. (This is a theorem of Milne; I learned of it from an article of Gamelin and Kislyakov, of which a [preprint version](http://www.mat.univie.ac.at/~esiprpr/esi710.pdf) can be found online.)