Could an actual mono black storm (Tendril of agony) deck be viable for Legacy?
A very brief answer to your last question: no.

A slightly less brief answer: the card draw and selection that blue provides, along with the additional "truly free" (it doesn't cost mana or a card) storm of Gitaxian Probe, is essential to the deck's viability, letting you find your key cards more consistently.  Also, while it wasn't mentioned, the red cards (Past in Flames and/or Empty the Warrens) allow for a viable backup plan when you can't get enough storm to consistently Tendrils for lethal.

Could you build a mono-black Storm deck?  Yes, at least in principle, in the same way that you could build a mono-black burn deck.  Would it be viable?  Unfortunately, not in any at least modestly competitive play environment.