Well, maybe for some of the episode. However, I would be interested to hear about what else he could do before Spock's accidental discovery of a computer problem. The experts had already analyzed the computer system, and found no problems. All the evidence showed Kirk to be guilty. The only evidence to support him was his past reputation, but any human can fall from grace.
Cogley had already recommended to Kirk to take a plea deal, and he would have done his client a proper service as a good lawyer if Kirk had given in. That was his responsibility as an attorney to do the best he can for his client with the case as it existed.
But, in the end, Cogley won his case using logic, intuition (Finney's daughter's forgiveness of Kirk played into that) and particularly trust in his client. Since he believed in his client, he realized that, with all other explanations being shown to be impossible, the only remaining possibility ( no matter how improbable) must be the correct conclusion. Also, before he could even prove that, he had to convince the panel (using an impressive speech) to allow more evidence to be presented, after he had closed his case.
The speech, the logic, the intuition and the trust strike me as a whole lot of function to go along with the form.