They’re there so that pedestrians can cross the street without stepping into it. The technical reasons are different, but I believe the driving force is the same: the arbitrary socioeconomic stratification of society to facilitate authoritarianism.

It's because the street was also the sewer. I'm not sure I buy your socioeconomic stratification/authoritarianism argument, especially since I doubt that even equites were routinely riding around instead of walking within the city. In much the same way it isn't worth riding a bike instead of walking for really short trips because of the hassle of unlocking and locking it, a horse -- let alone one pulling a cart -- wouldn't be worth it for any but the most ostentatious because Pompeii simply isn't that big. By the time a rider got the damn thing saddled or yoked, a walker could be across town.

I mean, to be sure, Roman society was authoritarian, but I don't think the crosswalks were necessarily a symptom of it.