> Is this mostly an anthropomorphization of the events

Yes.

Basically everything is bumping around until the desired reaction or configuration is obtained. The irrelevant proteins are generally not shown.

The length scales involved are extremely short so the chaotic soup works itself into configuration shockingly quickly.

There are also membranes, vesicles, and organelles (e.g. Golgi) that partition, package, and redistribute proteins so that they tend to be more concentrated where required.