when to run up and check the prop

I fly some high performance, complex singles like Saratogas, Lances, C182RG,
C206, and the like. Typical flying days have multiple hops while seeing
customers. On one hand I know pilots who say that you should do a full run
up and prop check before every take off, because the checklist says to. On
the other hand, I know pilots, mostly owners of similar aircraft, who only
do a full runup and prop check on the first flight of the day. Their
rationale is that doing it four or five times a day is unnecessarily hard on
the engine and when its been flown in the last few hours there's no need to
cycle the prop more. They argue if there's a new problem during the day
like a mag, its easy to detect upon first throttle up as you take off. You
would hear and feel the engine roughness and see its not developing full
power.

Are there any good arguments out there based in science and fact and not old
wives tales to support only doing a run up and prop check on the first
flight of the day ? I'm talking about a situation where you're flying
multiple flights a day and the engine never completely cools off.