In my opinion the compression plug does play a structural role, if designed to support the backside of the steer tube it helps protect a carbon steer tube from crushing or cracking. I think the Pinarello plug, shown above, is similar to the Colnago plug, and when set behind the stem clamp supports the back side of the steer tube.
The first example "already in the fork steerer" looks like an FSA plug which does not offer as much support.