I suspect your vision of aviation being so chancy is relative to your ability to mitigate the risk
First, I see (scheduled and high end corporate) aviation as having a very high reliability (ie not all that "chancy" as you put it) - the daily successful total of operations provides evidence of that. Caveat - this is not to say that GA has an inherent lack of discipline and safe history - only that it covers a far wider range of activities wherein the less safe taint the statistics of the more safe.
Secondly, if one intends to pursue a strategy other than SOP (and this either can be in respect of managing emergencies or planning non-typical operations), one needs to be able to quantify the risk in order to mitigate it with a reasonable degree of confidence. The necessary safeguard with this approach is that the approval signoff has to be elevated to a level appropriate to the assessed risk - ie often the PIC is not the appropriate level to authorise the non-standard operation (for the planning situation).
In those cases where such quantification is either impractical or time does not permit adequate research
(a) the solution gets progressively closer to the "wing and a prayer" style of management
(b) the SOP approach remains, in all likelihood, the preferred option.
As one who works in a particular environment where "risk mitigation" is a routine buzz phrase, I see many instances of good intentions based on qualitative gut feelings - not quite what the paradigm intends to be the case but better than just winging things on the day.