If you're the 'typical' straight male, perhaps not. But if you consider such imagery offensively exploitative and heterosexist, then, yeah, it's not such a good thing.
You're correct, the dual identity has been done to death as well--but, the main difference between that and typical barbarian fare (in my opinion) is that more readers are drawn towards it, and so the stories that rely on it frequently last longer (e.g., Superman, which has been with us for 75 years). I've never met a kid--either during my own time growing up, or in the years following which have been spent working in the childhood education field--who honestly felt like a He-Man or Superman in their daily lives; however, I think we have all fantasized about having secret powers, or being stronger than the bullies on the bus or what-have-you. That's why so many people relate to the dual identity trope, I believe--it enables the consumer to imagine something greater for him- or herself.
As one example, specifically related to MOTU, numerous non-heterosexual fans have explained in various threads over the years how they specifically related to the Prince Adam character because they simultaneously identified with the pressures of keeping a life-altering secret from those they loved, and they longed to "have the power" to overcome those who torment(ed) them. If the story had just been about a He-Man who was, for all intents and purposes, a hermit that ran around slaying demons, there's an entire section of the current fan base that would never has been as invested.
As for your comment about Adam being a "wimpy prince who can secretly turn himself into something he is not," I find that statement to be in the same vein as those who insist that the "She-Ra" cartoon series was "girly" and frivolous. That is to say, I consider it a false assumption. Just as the "She-Ra" series was far darker and more violent than the "He-Man" cartoon, Prince Adam was far from a wimp pretending to be something he wasn't. Just the opposite really: He-Man is who he is in actuality, whereas the Adam persona is a masque he is forced to wear--by the Sorceress--to protect his friends and loved ones. He doesn't want people to think he's lazy or inept, especially his father, and yet he has no other choice. How can that extra level of personal turmoil not make the character more interesting?