I have 100 enchanting and smithing and I am a Spellsword, originally pure destruction magic.
I own a killing machine of a Daedric Sword that absorbs health and does fire damage, but never runs out of charge.
I wear a full set of Daedric Armor with dual enchantments, with the helmet, armor, necklace, and ring with 25% less destruction cost each.
I think that the 100% destruction cost enchantment stops the sword from running out of charge. The sword absorbs 30 points of health and does 30 fire damage. When I was in a... quite strange situation that I didn't save, fighting Cicero with just the sword while he was wearing enchanted Dragonscale, the weapon lost charge. also, when walking around with my weapon drawn, NPCs tell me to "Be careful with that fire!" therefore I think that flame enchantments count as destruction magic, and to give further proof of that, I have a destruction perk that makes enemies flee from fire at low health, and that happens sometimes to the very few of those who survive a couple of strikes from my blade. I am not sure if fire is the first or second enchantment, or if that matters.
Am I the first to discover this? and is this a glitch or is it intended?

It is possibly a bug. If you are the first to discover it is not a real question. The question rather is who actually still cares about the many, small bugs of the game?

Have you tried recharging the weapon yet?

If it turns out to be a real problem then just go back to an older save file. You will certainly have some save file around?!

Only if it is game-breaking might Bethesda care about it. And from some bugs, that I find game breaking (infinite stats potions for example), did we still not get a fix.

its more of an exploit because it has a positive effect, and it doesn't have the recharge option because it is fully charged.

It's because you have 100% cost reduction. Reducing the cost of a school also reduces the charge-cost of enchantments in the same school, more people need to read my thread on playing an artificer
http://www.gamesas.com/index.php?/topic/1312501-the-way-of-the-artificer

That should not be that way. I know that it is, it just should not be. Enchanting is Magic for Dummies and only the Enchant Skill should affect Charges used and Spell Power. Enchanted items derive their power from the Soul Gem, not the Mana of the user.

Pretty sure that is working as intended. Your Destruction skill also determines the amount of charges you get for a Destruction based enchantment, so it makes sense that it would reduce the cost of each strike to 0 with 100% reduction.

I did a similar build with daggers instead of swords, was really fun.

Sounds like the game is confusing magic skill with the magic cost. Magic cost goes down with greater skill, but amount of charges is supposed to be dependent on magic skill not magic cost.

Ya this bug has been mentioned before. I know I read about it on UESP Wiki. Just being able to obtain 100% spell-reduction seems silly enough, not to mention the side effect it has on cast on strike enchantments of their respective school.

A test would be to see if any non-destruction effects work with 100% cost reduction enchantments of the respective school; i.e. a weapon with soultrap and apparel with 100% reduction in conjuration. If it DOES NOT work, then the OP's discovery is most certainly a bug. If it DOES work then it might possibly be the intent of the developers. If the latter is the case, I would say that was a very poor decision on their part.