Why don't B747s start takeoffs with full throttle?
The other answers are spot on, but I'd like to address one part, which is the "later down the runway." It is by no means "later."


(YouTube)

In the frame grab above of a 747-400 (taken at 1:12), the captain had already called out "takeoff thrust," the TO/GA system had set the pre-programmed thrust setting, and the 747 wasn't even at the piano keys. (Auditory cues can be misleading to passengers or air side spotters.)

Typically, a low thrust setting is set to make sure all the engines are responding in the same way, and more importantly, will have uniform application of thrust thereafter. This can be done with (standing takeoff) or without the brakes on,$^1$ or during a rolling takeoff. Then it is TO/GA time. (In tail-wind conditions, the procedure may vary.)

Here's another video by JustPlanes from inside the cockpit. Again TO/GA was pressed while the plane was at a crawling pace far from being anywhere later down the runway.



$^1$ Boeing 747-400 FCTM § 3.4