For instance, in a world where there are laser guns, why would anyone ever decide to use a sword? Outside of a person like He-Man, who has special skills and a special sword, no one would use these melee weapons. So realistically, warriors wouldn’t use both of these weapon types (as is the case in our world, after all, when’s the last time we saw a marine charge into battle with an axe?). Issues such as these, as well as personal preferences, led to the ground rules which follow.
I don't understand your train of thought. Ofcourse people would still use melee weapons in a world with laser blasters. Why? Well lasers are only light, and light can be reflected. So using a blaster against someone with great skill would be futile, and if you're locked in hand to hand combat with someone, a few melee weapons at your disposal would probably work better than a blaster.

In the vast world of Eternia, He-Man is not the only one with special skills. Infact I would like to think of He-man as rather clumsy with his sword. I'm sure there are many great beings in Eternia who could top him in swordsmanship.

Its great that you both have your own vision of MOTU, but it seems to me that while in cutting out what you don't like, you're stripping MOTU of some really important elements.