I'm curious to hear what these advantages would be ... not saying there aren't, just having a hard time thinking about what you might mean.

Getting to your destination faster. Driving slightly faster than the speed limit, keeping less distance from cars, cutting them off, etc.

I'm not sure if anyone would be willing or able to reprogram a self driving car to do that. But I do think its plausible people would abuse self driving cars. E.g. carelessly walking into traffic knowing the self driving cars will reliably still stop and be passive.

Keep in mind that self-driving cars will be loaded with sensors. Car's will basically be running continuous surveillance on their neighbours, and any "rogue" car will probably be reported by surrounding vehicles.

It is no different to a human driver deciding to speed.