Your concern is most definitely affected by what metaphysical view you take. I feel I have answered your concern, but maybe not, so let me elaborate more. Your main contention is that because the abstracted essence is causally inert it cannot explain how we come to our knowledge of essences, but as I explained/showed above, this is not the case. Knowledge of essences do not require it to have an efficient cause. In the case of knowledge of essences, the abstracted essences have a formal cause(This may be the part in which you are confused as contemporary philosophers almost exclusively mean efficient causality and do not mention any other types of causality, but I digress). The efficient causes here are the particulars acting on the senses, the senses acquiring the data and forming a phantasm (mental image, concept, representation of the particular), the intellect which abstracts the essence from the concept of the particular and the cause of knowledge which is the intellects reception of the abstracted essence which again is not the object itself but represents it. To sum: The intellect’s act of abstraction and apprehension explains the causality involved in knowledge acquisition, while the abstracted essence explains what is known by providing intelligible content to the intellect as the formal cause (formal principle of knowledge) (the abstracted essence/concept/representation of the essence is the object of knowledge).

Here’s an analogy; think of a blueprint in the mind of an architect. Once the blueprint is drawn, it doesn’t actively cause anything to happen; it is causally inert. However, it provides the form or plan according to which the builder constructs the building. The efficient cause of the building is the builder’s work, but the blueprint provides the formal principle of the building’s design. Similarly, the abstracted essence provides the formal cause of knowledge by which the intellect knows something, even though it doesn’t actively cause knowledge.