The base functionality of the OpenLog classes does not include writing to the Agent log, although that would be easy enough to add as a customization if you wanted. See the MailLogSubclass script library example for an example of using a subclass to provide custom functionality.
While you're correct that the AgentLog allows you to see what happened without having to "trawl through a log database", it also gets overwritten every time the agent runs. The whole point of the OpenLog database is to write everything to a central place, and store it somewhere.
But, like I said, it would be easy enough for you to add if you want. That's the great thing about having the code exposed in the database.