So far I believe side-effects as we think of them are unavoidable[1]. But they can be reduce to a minimum (the maximum being writing programs as a big set of global variables, and jumping GOTOs between mutations). Using functional style avoid a lot of nasty side effects like unnecessary temporaries, uninitialized values and their modification afterward (local assignments or across procedures). This is a thing one can do in C, whereas in FP languages, you're constrained to write this way, giving a culture of combinators and patterns (tree rec, map, fold, streams, monads, ..) hugely solid and tiny, thus reusable.

I understand what you mean, because even though I love FP a lot, I still struggle to conceive whole systems (other than simple map-filter dataflow ones) this way. So far I keep the FP principles for small pieces, hoping later on I'll find a way to close the gaps.

[1] John Backus tried to design purely functional languages a long time ago and he hit the IO wall (he mentions it in some article). Haskellers had issues at first and found that Monads were a nice functional way to express IO-like logic. It's still something weird, a lot less clean than purely functional expressions to be evaluated.