Could there be a way to one-click start an experiment for any feature? I know there is a hint to start an experiment for a recently created feature on the Analysis -> Experiments page which pre-fills information from the feature definition, but I haven't found one for previously created features

do you mean to create the experiment report from an feature with an experiment rule?

On the feature pages there should be a "View Results" button for each of the experiment rules. That will show the same pre-filled modal. We still need a little info, like which goal metrics you want to add, so it's not truly one-click, but close.