Re: "Is geometric distortion (purely optically) controllable through lens design? i.e. one 35mm or another; one 24mm or 21mm or another, can have more or less geometric and perspective distortion?"
The second question is straight forward... so I address that first. From a user perspective when comparing one lens to another there may be noticeable distortion differences and/or different levels/types of aberrations. In theory if one lens is "better" than another, one might conclude that one lens design is superior to another in a given system... i.e. lens design makes a difference.
Assuming that we are talking about (camera system) optical distortion without software manipulation, the quick answer to is it controllable is: yes. Will it be perfect: no it will not.
My understanding is that a certain segment of users were manipulating the results after the fact and so the camera mfgs. just automated the function... also as a way to sell 'inferior' lenses a top price. Another factor is that the gains in sensor quality demand "better" lenses to wit a quick fix is lens profiling. For what ever reason it's not going away, and if I was part of a group of users impacted by this I would prefer to have and use a original mfg. solution... as a starting point...
Casey