No most of the Venerated is doing rioters and fires/garbage and giving 25 bread or 1000 gold or protestors.
When i find raiders i will do them too when i get a chance.
5 Rioters a day maintains the loyalty where you are. So anything you do above that is a gain. I just done the 5 rioters a day and then the extra when i felt like doing more. Just a little a day can get you far.
And stop looking at your loyalty status every few arrests. Just set a goal for the day, like 30 minutes or a hour. Then look at the end of the session.