That skill may have been created after the skills for A/E had been determined.
However, unarmed combat is reflected in the primary skill; as I recall, the idea behind the secondary skills for that option are essentially added benefit in case you have a weapon equipped. But it just considers the highest skill instead and assumes you have that type equipped right now.
No, the concept of fighting an opponent unarmed is reflected in the use of the Strength skill. That's essentially what you are trying to do with your strength; fight your opponent. You receive a bonus if you also have a weapon (skill.. since it does not currently check if you have it equipped, too).
Yes. There is also a difference between someone with just a high strength, and someone with high strength and skill at dodging, etc. It isn't designed to emulate combat; it is just a basic skill check to give some ability to fail. Either way, this is not the suggestions forum, and as far as I know this is a restricted topic anyhow, so that's unlikely to change anytime soon.