The short, oversimplified answer is that Berber languages merge their "oblique" and "nominative" in much the same way that English merges its "oblique" and "accusative". Plenty of other languages do something similar, like most of the Northwest Caucasian languages. There's nothing magical about oblique and accusative that forces them to be merged when coming up with a two-overt-case system.
From a quick search, as I understand it, Berber is at least sometimes considered ergative-absolutive, not nominative-accusative, or at least more like E-A than N-A. While it doesn't match the facts of, e.g., Basque exactly, simple constructions give one case ("ergative") to transitive subjects, and the other ("absolutive") to both objects and intransitive subjects. And the objects of most prepositions get the "ergative" case. (There are even analyses that insist that Berber's "cases" aren't even really cases, although that seems to be a minority view.)
At any rate, however you analyze the "subject case" in Berber, the one that occurs on the subject of most simple transitive sentences, there's no reason that can't be the same as other cases. English assigning what looks like accusative case to the objects of most prepositions is hardly universal. Whether you prefer to describe English as having created an objective case that subsumed accusative, dative, and oblique, or as having merged accusative and dative into oblique, that's not the only way to get to a two-case system. And patterning transitive subjects with objects of (some) prepositions is one of the many other ways, attested in multiple languages (although mostly E-A languages).
Finally, I don't think Berber is usually analyzed as having case prefixes. Your "a-" and "u-" prefixes only work for the first class of nouns; you can't describe the other classes ("tarbat/terbat", "iles/yiles", and "taddart/taddart") with the same prefixes. What you called the "accusative" is considered the base form ("free state"), and the nominative or ergative or whatever ("construct state") is described as formed by vowel alternation rules (different ones for each class).
Exactly how you handle all of that in Case theory depends on how you handle ergative languages and how you handle case mergers. A system that can't handle anything but English just won't work for Berber languages. Obviously a system that always assigns NOM to the subject position won't work for ergative languages unless there's a second layer than can then map NOM to ergative in transitive sentences and absolutive in intransitive sentences. But a system that can assign ERG in some languages and NOM in others, or that moves subjects to different locations (one ERG-assigning, one NOM-assigning) in different languages, doesn't need that. Whatever you do there, you can do a simpler version of for prepositions assigning case in various different languages. It's impossible to answer for all of the Case theories proposed for every version of GB and MP, but should be easy for any specific theory.