Maybe they realized how moronic it would look to have the same live-action actor playing both Adam and He-Man, or maybe they didn't want to pay for the special effects required to portray the transformation sequence, or maybe Dolph Lundgren refused to wear pink and white tights. For whatever reason, there's no Adam. He-Man is just He-Man.
This deprives us, of course, of the homoerotic transformation sequence: Surrounded in light and projected against the imposing background of the ominous Castle Grayskull (that way they can use the same sequence no matter where Adam is at the time), mild-mannered
As for the movie, at its climax, He-Man finally, finally holds aloft The Sword and shouts "I have The Powerrrrrr!" as he's enveloped in light, and...it doesn't make any sense. He never did that before and never does it again. It just comes out of nowhere, because it was in the show...even though the movie doesn't follow the show, since he doesn't transform. He just shouts and glows in light while Skeletor stands there thinking, "The fuck is he on about?" It goes back to how Cannon tried to have it both ways. The "I have The Power" line is so iconic they felt they had to include it, even though it doesn't make any sense in the context of their adaptation. (Think the last-minute nonsensical never-referenced-again "By your command" line in the Battlestar Galactica remake.)
Still, there's no Prince Adam. And we're all happy about that.