There is a lot (and I really mean a LOT) of evidence that what you wrote isn’t true.

Increasing the cost of something most definitely reduces the number of people who will indulge in it. That’s a basic economic principle and the basis of almost every episode of Gordon Ramsay’s Kitchen Nightmares. Cigarette smoking is down across western countries massively since governments started taxing the shit out of it. You have evidence right here in this article that sugary soda sales drop when you increase the cost. A 50c difference between Coke and Diet Coke is gonna mean that a lot of people start picking Diet Coke instead. Carbon taxes have been demonstrated to be an extremely effective way to encourage people buy more energy efficient cars. When you add an incentive, such as grants to purchase electric cars, insulation or solar panels the taxes on the bad stuff are doubly effective and can help fund said grants.

Now there’s definitely evidence that if the tax isn’t noticeable it will have little effect, but in say the Republic of Ireland where the difference between a Coke and Diet Coke is about 60c (thus pushing retailers to stock them separately and clearly label the difference) there has been a big effect. In the UK where the difference is only about 18p there has been less of an effect.

Of course you can say that this is a tax on the poor and you’d be right. Stealth taxes do hurt poor people more than anyone else. But they’re also the ones who benefit most when you couple taxes on bad things with relief on good things such as meat and vegetables. The most effective way to change people’s behavior is to hit their wallets.