It does and I'm aware.

However the primary reason to use it is to "load" a lot of damage into multiple single target spells and attacks on a champ who is going to benefit from more mana and MP5.

Corki and Ez, when played well, are not heavily reliant on their mana (excepting a few cases) or can be paired with a champ to reduce their mana reliance.

However champs like...

Yorick, possessing an AAR and a single target AD scaling nuke.
Pantheon, with a powerful AD scaling nuke and single target gap closer
Urgot, with a powerful and spammable AD scaling ability

Can utilize the entirety of the items uses, and are often encouraged to build some secondary mana sources (Trinity Force, Frozen Heart, Banshee's Veil) which amplifies the effectiveness of the item.

Just because the "primary" reason is something doesn't mean it can't be used for something else.

At level 18 Corki with a Triforce, Muramana is doing something like 150 damage (passive + active) per hit at max mana. At a mere 2100g, that's a lot more damage than a Bloodthirster for a fraction of the cost. Sure, Corki might not need the mana as much, but we're talking double the damage-per-gold efficiency of Bloodthirster here and he has no trouble charging a Tear.

one thing i want to point out before the manamune did not have cooldown but this one does 3 sec for 4 mana so if my math is correct it will take 9 mins about to get all 750 mana 9 fking min

I too think this item is certainly worth the gold, granting a whopping 180 maximum damage (60 AD, 120 magic damage at 2000 mana). However, I'm not sure when to build the thing. It takes quite a while to level it, and until you do, most of that gold is pretty much put aside when it could be used on valuable stats in lane.

So, if this thing is viable, when should I get the Tear, and when should I upgrade it into the Manamune? This is primarily when I'm playing Corki, BTW

My theorycrafting says it's best to get the Tear while still laning, possibly after the Phage or Sheen. It's cheap enough to where it's not that big an investment, and having more mana to poke with on Corki might actually make his poke stronger (though the lack of Dorans would make his all-in weaker). Definitely don't get it before 6.

Completing it after Triforce is probably the best bet as I see this as a Bloodthirster replacement, and after that possibly Black Cleaver/Guardians.

Mind you, I've only had two or three games to experiment with this on, and had a decent amount of success as a Corki/Sona vs Graves/Leona lane, where having the extra mana for poking benefited more than the lack of Dorans hurt as we certainly weren't going to win all-ins anyways. If we could arrange 4 or so people with which to run a couple of customs on it'd be nice.

You wanna know who should build this? YORICK. He has some mana issues in early levels, but build him into the utility tree and start with with a tear and philo stone, and you will be sustaining and making gold all freakin day long. Upgrade to muramana, triforce, and iceborn gauntlet? Dude...scary

I'd say it's clearly a viable choice.

The main thing holding up Manamune is that you need to get something like a Sheen for the AD to just end up being cost-effective for the item late game when you don't need the mana. Which is a serious problem concerning finished items that offer a handy passive for free (IE crit damage, PD movement speed). Now that you can add ~80 bonus magic damage with each hit (essentially Madred's Bloodrazors actual damage against something with 2k health), it's got a worthwhile free passive that not only makes up for mana being more or less useless on a late-game carry, but actually puts that mana to use.

I'm not arguing non-viability it's certainly compelling.

However I'm pretty certain that traditional carry items will still result in higher DPS more often. Manamune would be more of a luxury item in a game where you know you don;t need to optimize your build.

AND every cast, your spell damage is incresed to

Can you explain why you think that?

I'm not going to compare Manamune to an IE/Pdancer build, but as a replacement for Bloodthirster in a Triforce/Bloodthirster build I'm having a hard time seeing the downside in the long run. It offers more damage for cheaper. There's only three downsides to this build that I can think of, which are

-Weakens your mid-game until you finish charging the tear/Manamune.
-Less AD = less crits, but running the numbers this seems to be more than balanced out by the extra magic damage.
-No lifesteal.

With Dorans now falling out of favor due to AD having gotten cheaper in general (longsword start on ADCs seems to be getting popular now), even the weakening to the mid-game seems to be limited.