I don't know about Tornado Cash specifically, but every cryptocurrency tumbler that I'm familiar with takes a cut of the pork, on top of any transaction fees. This community discussion[1] makes it sound expensive.
> Besides that, let us not forget that the Mastercard/Visa middlemen charge us large fees for using their services and knows everthing about our purchase habits.
This is a common refrain, but it isn't quite accurate: the payment card networks charge merchants to use their services.
And sure, they know what you buy. But my Aunt Susie doesn't, nor does the next person who I pay using my payment card. Privacy as a concept is described by the security or threat model one is trying to conform to; cash and payment cards both protect me from unrelated prying eyes. Cryptocurrencies can also protect me from prying eyes, but they charge me for the privilege. By default, both my Aunt Susie and my neighborhood restaurant can see that I've been unfaithful and tried a new place for dinner.
[1]: https://torn.community/t/fee-how-much-does-it-cost-to-use/68