Okay, there's a lot here to address, so instead of directly replying by quoting, I'll just talk about the issues raised.
MoTU Setting:
The thing to remember about Eternia and the whole MoTU setting is that it was designed, first and foremost, to sell toys (like most cartoons in the 1980s). The best way to do this is to make sure you not only have plenty of action figures (who seem different enough to get kids to bug their parents to buy each new figure), but also provide a lot of vehicles and other settings. I believe this is the primary reason for the mixed fantasy/sci-fi setting.
It's also a bit disingenuous to see fantasy and science fiction as completely different entities. Sure, they seem like that on the surface, but there's a lot of properties that mix elements of the two, the most famous probably being Star Wars. A lot of people lump SW in with sci-fi, but it's really fantasy in sci-fi clothing.
Original Setting (i.e. the little comics that came with the toys):
I recall being very confused about this as a kid. I watched the cartoon every day and knew the characters quite well, but then these little comics presented a very different story. Like Tawmis said, He-Man was originally a Conan-like barbarian and had no relation to the monarchy of Eternia.
Also, he used an axe a lot (which is why there was an axe packaged with the toy) which he never used in the cartoon and his sword was given to him by the Sorceress of Grayskull (like the cartoon), but there was one huge difference between the sword in the cartoon and comics: Skeletor also had a sword in the comics, whereas he only had a staff (in the 1980s version; he did use a sword at times in the 2000s remake). The interesting thing, and I'm sure this was a marketing gimmick, is that Skeletor's sword was purple (as opposed to He-Man's gray) and both of their swords fit together to create one sword. It was weird.
Public Service Announcements:
MoTU had a lot of those PSAs after the cartoon (which were cheesy), but at least they had some relevance to the episode. In contrast, GI JOE's PSAs were wildly erratic and rarely had anything to with the episode's content at all. Plus, the GI JOE soldiers had no respect for laws, because they'd suddenly appear in some kid's house telling them to not drink bleach or something equally moronic. Then again, some kids a few years ago did try eating Tide Pods, so maybe the creators of GI JOE were on to something...
MoTU (Roles for Women):
He-Man and the Masters of the Universe was primarily a cartoon aimed at young boys, and as such, female roles took a backseat. The reverse was true for
She-Ra: Princess of Power (the 1980s version, not the SJW disaster that's on Netflix) where almost all the characters were female.
If you think about it, MoTU was quite progressive for its day because a lot of women held high positions of authority and were seen as extremely competent. Teela was the Captain of the Guard (although it didn't seem like the castle had many guards...), the Sorceress was an incredibly powerful magic user who kept order and could even shapeshift, and Queen Marlena wasn't just a royal-by-marriage, she was also an Earth astronaut and skilled pilot.
Secret Identities:
I really don't think the whole secret identity thing was necessary. Like Notbobsmith said, his parents were the King and Queen of Eternia, so being targets was par for the course. Anyone who lived in the palace would also have to realize that you're taking a risk by being there, but presumably also had the best security as well.
The real reason to keep people thinking Prince Adam and He-Man were two different people was to provide conflict and drama that didn't involve combat. I also believe that because so many superheroes did this, the creators of MoTU simply thought "this is how it's done" and didn't bother to consider anything else.
Interestingly enough, there are at least a couple of episodes where Prince Adam's mother, Queen Marlena, hints at knowing her son and He-Man are the same person. In contrast, Prince Adam's father, King Randor (who bears a
strikingly resemblance to the Burger King mascot) didn't have a clue.
Reusing Animation:
Filmation (the studio behind the MoTU cartoon) reused a LOT of animation, but there's a good reason for that. Hand-drawn animation is an extremely laborious process that takes months. If you can save a little time and money by reusing animation for parts that don't need unique animation (such as a character getting up or rolling on the ground), it's considered good practice to do so, especially since the intended audience likely wouldn't notice.
Big animation studios did this as well. Disney, for instance,
reused a lot of animation as guidelines. So if a company like Disney, which had a ton of money and manpower to throw behind each animated film needed to do this, you can bet a small studio like Filmation would do the same when creating a weekday afternoon cartoon designed to sell toys.
I only pointed out that, in cartoons and comics (and also in live-action films), women (and men) are often kings or nobility, or heroes/heroines of various types (which I labelled a, b, c, d). But you rarely see women (or men) doing normal everyday things, like peasants or merchants, unless they're there to be kidnapped, killed or robbed.
Granted, I haven't seen He-Man before. But what in what possible part of the multiverse would that even work? 
