In contrast to the brain's complex computations, priming has an easier analogy available: context. In human thought and behavior, the importance of context shouldn't be underestimated. Priming/context tailors results according to the situation. It's more complicated than a one-to-one mathematical function or a row of light switches. It's closer to sowing many seeds in proximity and allowing the plants to entangle.
In the same way, priming/context could be ubiquitous, occurring at differing levels. As reductionist as it sounds, pieces of brain have surrounding pieces to act as context. One brain activation "primes" its counterpart because it contributes to overcoming its activation threshold in the "present" or in the "near future"—keeping in mind that these slivers of time are much smaller than the smallest human-perceptible instant. And thereby a small cluster of brain activations primes the clusters connected to it. And larger clusters prime larger clusters, and so on into greater sizes.
Also, ubiquitous priming is an analogy of the value of the brain's structure. An item of information isn't just encoded in isolation but encoded to be additional priming for more items. From inborn instincts, information primes the brain for behaviors that are advantageous for natural selection. From cultural lessons, information primes the brain for the culture's focal points. From language, information primes the brain for the grammatical distinctions to match tense/mood/aspect/etc. From memories since birth, information primes the brain for recall of crucial episodes. Indeed, pushing the analogy into hyperbole, exactly how much of a human's identity, such as their preferences and goals and coping styles and experiences, can be thought of as their largest context, meaning their whole unique set of brain structures for ubiquitous priming?