I'm guessing that by the point in time when King He-Man comes about, Adam has grown up a little - physically and in maturity - to the point that he and He-Man are finally one and the same in their being and changing back and forth is unnecessary. Those in his inner circle probably still refer to him as Adam or King Adam, while to the general Eternian public, he's more popularly known as King He-Man.



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'Tis the wind and nothing more.....

). But Adora doesn't have family on Etheria. Hordak is already trying to destroy the Rebels/Whispering Woods every episode. He already wants to capture Adora, both because she escaped him and because she is leader of the Rebellion. I am hard pressed to think of one good, logical reason for her to have the secret identity. I guess Skeletor could find out if he comes to Etheria like he did in the cartoon, but that doesn't seem to be the case in Classics.
At least this way they could make the battle look good by having the Adora Clone come closest to besting She-Ra over all the other Hordesmen, which would help maintain Adora's standing with Hordak.) Something like that might work on those occasions, as has a Robotic He-Man until such time as Adam could get free & make the change.
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