its not math craft, its knowing hellion


it takes 6min untill money spended on a natural gives you benefits.
zerga proxy base , in-line-of-tank-fire +urly zerglings gives you a tec-headstart, witch allow flawless blow

what get stopped? you banchee or your banchee tec?
ofc you tec gets stopped, couse its to late, money have been spended on hallions, whit not benefit your current position.
banchee on itself not helps you either, 1 spore will counter it, its that tank you want

deffensive hellion speed only works if hellions are in the open, spotting light units / when your base is open for light-units to come in.
now like you say yourself, zergling is already there, and hellion can not spot them in the open.
when your hellion is in the open, its also a target, thats needs micro-cover.

a marine have 7ground dps / 35 life
a hellion have 7.6dps vs light units / 90life
you not pay/tec extra for damage or life, you tec/pay for speed
i beleave a tank is build as fast as a hallion, you can build that tec-lab at rex, before factory is finished, you have been granted whit a tank-tec-buff since hots
now you not fear that hatchery will finish, you wait for it, couse more shit to destroy before its cancelled,

If he's dumping all his minerals into a contain at the natural? Yes he is. Fast 3rd hatch and static defenses at the natural = not much money for building things at home. Also he keeps his lings near the natural to stop any attempts at breaking out. That means you have a big open shot at the Zerg's main/natural.

Hey bro, you don't know shit about the game.

so he give the win to you for free

he build cannon-food-hatchery under your main
he park zerglings under your main
he start droning for 2-bases, and builded 3hatchery's
he knows you are on 1 base

you have 3times more money for army as him
but what do you do? you make 2*AFK-cc and empty bunkers!