How does that stop people from still buying the now corrected-for-those-taxes garments? All you've done is added a revenue stream in the middle, and now there's even less incentive for regulators to do anything about the _actual_ problem, because now they're making (more) money off of the problem, and solving the underlying problem would damage those revenue streams.
The price correction is the point. If the externalities are internalized it makes better methods proportionality more incentivized and viable if say cotton fabric garments are only seventeen cents more expensive than a synthetic instead of the previous two dollars without environmental costs factored in. Demand would be shifted accordingly.