I noticed a difference when I moved from 'down south' to the Top End.
In the Top End, run-ups for the first flight of the day is something you do before you loaded pax and freight.
Partly because it is bloody hot and their was only three piston engined charter planes in the whole top end that had airconditioners (!) and secondly, it removed the temptation to say 'ahh, bugger it' if you actually found something wrong during the run up with pax on board.
The big problem with the argument we are having here though, is not which is the best single way to do things.
The problem is that too many pilots are just doing what they were taught, shown by someone who was just doing what THEY were taught!
Most of the suggestions above are the best answer, in a certain situation.
F'rinstance, mates who did dingo baiting in C206's out at Halls Creek used to do their runups rolling up and down the strip first thing in the morning. There was no hardstand, no stone free area, just lots of red gravel. There were also no aggies, and very few no-radio itinerants arriving at 7am!
Transfer the situation to Ngukurr, a sealed strip with half a hectare of asphalt as a parking area, with Kingairs and C402s arriving at all times of the day and night -- there was no reason to do runups on the runway. Arrive there to find someone doing runups on the threshold in their Chieftain and you come to the conclusion that they are either too dumb to realise it isn't necessary or too lazy to sweep the area under their props on the hardstand. By the way, how the hell are ya, H.E?
A third situation might be a gravel parking area with a sealed runway. Well, provided it is not a busy area or time of day, the threshold is the one place that can be relied on to have had all the loose stones blown away. But why not put yourself on said threshold at an angle perhaps into wind (!) that allows you to keep an eye on downwind, base and final, just in case?
Use your head! Prioritize!
(1) don't put yourself in the path of a landing aircraft
(2) don't inconvenience an inbound aircraft, broadcast, listen, and vacate if necessary,
(3) then start thinking about taking care of your prop, etc.