Armor is inherently restrictive
The Armor section says:
Medium or heavy armor slows the wearer down.
No reason given; it's just what armor does.
The Carrying and Movement section says:
Like armor, a character’s load affects his or her maximum Dexterity bonus to AC, carries a check penalty (which works like an armor check penalty), reduces the character’s speed, and affects how fast the character can run...
If your character is wearing armor, use the worse figure (from armor or from load) for each category. Do not stack the penalties.
Though the mechanic for armor encumbrance and encumbrance from weight are the same, they are separate systems; the one does not inform the other. Chainmail, a medium armor, weighs more than banded mail, which is heavy. Indeed, if verisimilitude is a factor, the very musculature of such a strong character might encumber it.
You can remove the penalty:
...can move at [his] speed even when wearing medium or heavy armor or when carrying a medium or heavy load (unlike other creatures, whose speed is reduced in such situations)
A binder (Tome of Magic, p9) binding Aym (ToM p25) gets Dwarven Step:
You can move at normal speed (without the usual reduction) in medium or heavy armor.
And any character equipping the Tooth of Savnok (one of the Teeth of Dahlver-nar, ToM p79)
...move at your normal speed when wearing medium or heavy armor or when carrying a medium or heavy load (unlike other creatures, whose speed is reduced in such situations)
Really ignoring it
Ignoring or altering the mechanic is not significantly game-breaking, but would reduce the value of any mitigating factors, such as those above, and enhance mobility.