I don't think you are missing anything. I expect most players who use melee, pick only one of the three skills as a major.
Some might argue that since h2h can't be disarmed, it could make some sense, but there are plenty of quest items or bound weapons that can't be disarmed either to get around that. Some players, for role play reasons might want to be good with a couple melee skills. The game is easy enough that supporting that is not hard to do.
Even farther afield and abandoning many conventional assumptions about this wonderful game are those of us who choose majors based ONLY on controlling how fast and how high we want to level. My mystic archer is a 'glass cannon' who refuses to touch a melee weapon or use h2h, yet has all three as major skills. Those three melee skills, along with speechcraft, are four majors she has that she will never use.
-Why? Because she never wants to level above 20, and wants it to be a very slow trip to get there.
-Why level 20? There is nothing in the game
we want that requires a higher level; in fact by level 30, there is nothing new in the game at all except the same foes with more hitpoints.
-What about strength bonuses, which will be only +1 if you never use those three skills? For role play reasons, she will never boost strength above her base value of 30, so she doesn't care (strength doesn't help her magic or bow and we
like the challenge of carrying less loot / getting rich slower).
-Way off the beaten path, and not for everyone? You bet.
-Do we enjoy playing that way? Immensely!
If you are playing more 'conventionally', you are probably best choosing only one melee skill.