Let’s go over the items:
Tear of the goddess:
+350 Mana +7 Mana Regen per 5 sec UNIQUE Passive: Each time your Champion uses an Ability their Maximum Mana will increase by 4 Mana, up to a maximum of twice in a six second period; bonuses cap at +1000 Mana.
BB doesn’t activate tear, so you only gain + mana when you throw your Q. Your +mana gain is minimal until you have manamune.
When you finally have the farm for manamune (2110 gold, and you need at least level 1 boots before then, so let’s say 2460) On a good game, would you estimate this to be 12-15 minutes, if you do very well?
Manamune:
+350 Mana +7 Mana Regen per 5 sec +20 Attack Damage UNIQUE Passive: 2% of your max mana is converted to attack damage. UNIQUE Passive: Each time you attack, you gain one maximum mana (3 second cooldown.) Each time you use an ability …
At this point, your Q is still giving you 4 mana per throw, and auto attacking is giving you maybe 20 mana per minute MAX. It will now take you 50 minutes (at maximum speed) to use auto attacks to fill your mana. Let’s say you throw about 2 Q’s per minute (160 mana a minute usage, which would mean you need runes etc to keep up, and in addition to the 7mp5, and you aren’t using bouncing blades), that’s a whopping extra 8 mana per minute you’re accumulating. Let’s say you did that for the 12 minutes you were farming - that’s 96 mana (or 1/10th of the way there.) So, in this case you’ve got a very long way to go before manamune comes to full potency.
In most games, you will not farm that fast, nor will you auto attack every 3 seconds to proc manamune.
This is the same problem ashe has, where she can have a 4 second volley time, but can’t proc manamune enough to make it better than just buying a BF sword.
I’d rather have my AD and mana regen up quickly via a BF sword and a meki for 2240, and have that big damage boost at the 15 minute mark.