No. VAT is meant to control prices.
If the government would not want to control prices then it would not have VAT or tariffs, it would just have 1 type of tax, and that would be it.
The reason why we got VAT,tariffs, income tax, etc is because they want to control the entire economy. That is not a free economy /free market.
Sorry but your logic fails.
I reiterate Webster's definition of "free market" -
which you expressly agreed with:
" an economic market or system in which prices are based on
competition among private businesses and not controlled by a government ", my emphasis.
You need to show that the Gov. is somehow directly controlling prices "among private businesses" - who to my knowledge do not pay GST or VAT - such as thwarting price dumping which stifles competition.
Instead, you seem to be arguing for
a completely unregulated market, which however is not supported by the definition. Indeed, I could argue that the gov. is controlling the oil price by warring; or that a mosquito farting in the jungle turns into a hailstorm destroying crops controls prices; or that a company employing "slave labor" moves into an area and dumps prices controls prices - the definition is however much narrower.
Besides, even if you managed to show that it's not a free market according to the definition above, you still need to show that the money paid for GST or VAT, in turn, was not competed for and not put to good use, such as infrastructure, education, medical etc. and that a completely unregulated market would have disposed of those resources more efficiently - good luck!