VAT is common worldwide. About 80% of economies have one. Having a VAT doesn't preclude a free market. The countries with the highest economic freedom scores (Singapore, Ireland, Luxemborg, New Zealand, Switzerland) all have VATs or GSTs.
VATs are not "similar to tariffs".
VATs are a general tax on consumption, not on trade.
That means that they apply to all goods (domestic or foreign), and thus increase prices/reduce consumption generally. Tariffs only apply to foreign goods, increasing prices/reducing consumption of imported goods (or domestically produced goods that include foreign-sourced materials).
Quoting from the Cato Institute:
So why the misleading comparison? The VAT line gives cover to protectionism under the guise of “fairness.” If you can convince the public that other countries are taxing us and we’re not taxing them, then tariffs look like a justifiable policy correction. But the economics are clear: VAT is not a tariff, and tariffs are not a consumption tax.