Supposedly Cogley had studied his Matlock tapes carefully: it's all about the delaying act, the filibuster that gives the private eye time to turn the case on its head...
However, why should this surprise us? It's not as if Kirk picked his defender out of a pool of promising prospects. Instead, he was pointed towards this fool by the prosecutor
. The chick that wanted him to fry. And it would seem Stone in turn hand-picked Shaw to make sure that Kirk would indeed burn brightly.
I guess Kirk could have challenged everything on the basis of bias, but would that have helped his case? He went in confidently and swiftly, probably both because he thought that evidence would prove his innocence, and because he was loyal to the service and wanted to keep things as quiet and local as possible just as much as Stone did. This backfired big time initially - but had he insisted on a fair trial, held outside SB11 later on, things would have been much worse, as Finney's devious plot would have been carried to its conclusion: Spock would have lost access to the evidence, Finney would have snuck out of his hiding place and disappeared, and any verdict would have been a damning one for Kirk's career.