Most SoCons would be more likely to identify as "limited government", rather than "small government".
That said, California has always been more aggressive with Jaywalking than east coast cities, at least in part because of a quirk in the state vehicle code that gives the right of way to a pedestrian in a crosswalk, marked or unmarked pretty much all of the time. The linked article is pretty clear that the primary motivation for tasking their traffic officers with jaywalking enforcement is the negative effect it has on traffic. I drove through this part of downtown just the other day, and it was pretty clear that the jaywalking was out of hand just in terms of moving in a straight line. Forget about trying to make a turn.
Do you think that people could be made to cooperate without enormous fines? Maybe use this horde of cops to interact with the public, gain willing cooperation?
Gee, that just might work.