I'm pretty sure that Elfangor giving the Animorphs the cube from the get-go would have been a TERRIBLE idea. And Elfangor must've known that.
Keep in mind, he'd just dumped an interstellar war into the laps of five kids. They had plenty on their minds, just trying to figure out what to do next. Handing them a giant security risk (which would effectively doom the world if they lost control of it) on top of all that? In no way would that have been a good idea.
Not to mention, Jake started out the series not even realizing his brother was a controller. He could have tried to hide the cube in his room, and bam, the war's over, right there.
I am a little surprised, though, that the Yeerks never found the cube before David did. Didn't they mention having scoured the construction site to eliminate any evidence that aliens had been there? Lol, they didn't do a very good job.