Q:

Why is attacking from higher ground an advantage? 

I just don't understand how attacking someone from higher ground is an advantage in melee combat.  I always think of two examples where I can't see this to be an advantage. 

Example 1: A kung-fu fight in a room.  If I stand on a table but my opponent doesn't, how is this an advantage?  I increased the reach between us, punching him requires me to bend, and a kick coming from higher up is not harder to block or dodge. 
Example 2: In a sword fight, a knight is on a rock.  You can strike me from above, yes, but I can strike your legs more easily.  Again, you'll have to bend over to block and attack.  Again, the the reach between us is increased. 

If small opponents get bonuses to attack and defense because they're small, what sense does it make that becoming "taller" (i.e., having higher ground) suddenly gives me an advantage over you? 
Most systems I know give you an advantage if you are on higher ground – why? 

A:

I'll deal with your first example first: standing on a table in that situation is not particularly an advantage.   It's also, therefore, very unlikely behaviour for a martial artist.   (Not counting Feng Shui players).   Standing slightly up from your opponent, on the other hand, is an advantage for many of the reasons below.   It brings your kicks to better target points with less effort, while costing you nothing. 
Historically, however, standing on tables or fighting indoors is an unlikely scenario.   Let's discuss the more common swordsman (or in your example, armoured knight) fighting uphill against similar opponent.   In this case the higher-ground advantages are huge.   
(To help make examples clearer: our swordsmen are on a hillside.  Tom is higher up, Lowry is lower down and facing uphill.) 

The assumption that Tom needs to 'bend over' to block is false.   The leg guards work perfectly well while standing in a normal fighting crouch, regardless of the origin height of the attack - it has to be at Tom's leg height regardless.   At worst Tom ducks slightly. 
Lowry, on the other hand, gains defence for his legs but loses it at the head, and loses access to attack Tom's head.   Is this a fair exchange for Lowry?   No!   (Hint... which would you rather lose, leg or head?) 
Endurance matters!   The defence advantage for Tom is large.   Tom needs to guard his legs and abdomen more... some of the least tiring guards, because your arm drops low.   Lowry needs to guard his head more... needing him to lift the weight of his weapon more often.   And he has to block against greater force, because Tom has gravity aiding in the downswing. 
On this theme, gravity is Tom's friend.   Most styles use more cuts down than up, for a reason - those cuts have more power with less muscular effort.   (And for the beginner, cuts down are also easier to execute and to feint with.)   Lowry also has to lift the blade more to perform equivalent cuts and thrusts. 
Footwork matters!   In a duel both fighters move in all directions.   Stepping backwards uphill leaves you less likely to trip than stepping backwards downhill.   And more likely to catch yourself before dying.   (In a massed formation during battle the rules are different, but that applies to most things.) 
Balance matters!   If both are competent, neither fighter will particularly lean forward or back... or they'll lose.   (Tom ducks down, not leans forward, to strike the head.)   
Reach really matters... but only to the key target points.   All else being equal, on a mutual thrust, Tom hits the head while Lowry hits the calf.   Guess who's limping away from that fight? 
For armoured knights with swords the situation is even worse, because the legs and chest are very hard to injure on a man in harness.   (That's what the armour is for, after all.)   The good target points on a suit of plate armour are mostly upper body.   (Although this match is historically unlikely outside competitions; poleaxes would make more sense, and are slightly more even because of the leverage advantages they grant.) 
Vision matters!   As wraith808 correctly says, looking up is harder than looking down.   And it's a lot harder if you're wearing a helmet.   Lowry has to work harder to keep his eyes on Tom.   And can more easily be distracted by attacks coming at the head. 
Speed matters!   When Tom attacks he's closing the distance downhill, with gravity aiding his strike.   Lowry is climbing to do the same. 

All this only applies if the height difference is a couple of feet, or a not-too-steep-hill.   At more than that this isn't a swordfight as such; Tom is hacking down at a climbing opponent. 
This is a summary of a complex issue... but the purpose of game mechanics is to summarise complex issues.   A flat bonus is not an unreasonable representation of this effect. 

A:

There are two real world reasons I can see:

To strike something above you, you have gravity working against you. 
To strike something below, you have gravity working with you.  
Your balance is better when leaning forward than when leaning back. 
When striking something above you, chances are you'll lean back and
vice versa. 

As for inclusion in a game system, I think it makes for interesting tactical game play.  The mechanic is simple to apply as no complex questions have to be answered.  
As for small characters, you can keep adding rules for everything but the system gets unwieldy.  As a designer, you pick and choose which rules make the game feel more fun.  As a GM, you should add and remove rules to fit your group.  It might be that elevation doesn't work for you.  Talk to your players and house rule it if everyone agrees. 

A:

Higher ground has some general advantages that the bonuses you refer to might take into account:

Elevated ground gives a better view of the combat, even in melee situations.   Looking up towards a combatant in general obscures intent more than looking down does, especially since most attacks originate from a higher elevation. 
The combatant on the higher ground will in general tire less quickly, and have more mobility both for attack and defense. 

It is not always an advantage, but modeling a combat system of generalities, it would in general be considered to be more advantageous than not. 
With the combat related reasons for out of the way, there is the strictly literary reasoning.   The other reason that high ground might be included as a bonus, even when it might be interpreted not to be is that the advantages of high ground have also been exaggerated in fiction as a trope.   Thus, with all of the tropes that are commonly seen in fictional settings, that one is reinforced also.