I personally know of two cases where a DUI resulted in a person being let go; one of them at a brokerage.
It just seems rational that there would be a civilian version of "conduct unbecoming"; this would describe a situation where one's actions are so far beyond the pale of acceptable behavior that an employer is well within its rights to terminate the individual's employment. It might be a reputational risk to the firm, it might be something that raises serious doubts about someone's judgment, it might be tied to someone's place within the firm, et cetera.