There is, as far as I can tell, and enormous amount of accidental complexity in software. Far more than there is inherent complexity. From my personal experience, this largely arises when no time has been taken to fully understand the problem space, and the first potential solution is the one used.
In that case, the solution will be discovered as partially deficient in some manner, and more code will simply be tacked on to address the newfound shortcomings. I'm not referring here to later expansion of the feature set or addressing corner cases, either. I'm referring to code that was not constructed to appropriately model the desired behavior and thus instances of branching logic must be embedded within the system all over the place, or perhaps some class hierarchy is injected, and reflection is used in a attempt to make make the poor design decisions function.
I don't think adding features makes software more complex, unless those features are somehow non-systemic; that is, there is no way to add them into the existing representation of available behaviors. Perhaps an example would be a set of workflows a user can navigate, and adding a new workflow simply entails the construction of that workflow and making it available via the addition to some list. That would be a systemic feature. On the other hand if the entirety of the behaviors embedded within the workflow were instead presented as commands or buttons or various options that needed to be scattered throughout the application, that would be a non-systemic addition, and introduce accidental complexity.