Germany has a reduced rate for certain goods but in practice it is pretty arbitrary and mostly the result of lobbying. Note that even if it were applied entire

Germany has a reduced rate for certain goods but in practice it is pretty arbitrary and mostly the result of lobbying. Note that even if it were applied entirely consistently and without bias it would still only reduce the regressivity, it wouldn't make it non-regressive. If a person with low income buys a gallon of milk they pay the same VAT on it as a person with high income would. If they buy cheap off-brand cheese they pay the same VAT rate as they would pay for expensive luxury cheese (except they likely can't afford the latter). VAT doesn't account for income inequality, it just makes everything more expensive for everyone. Income tax OTOH impacts high income households more than those with low income. At least in theory: in practice income tax (especially in the US) has massively gone down for high income households, again just affecting everyone equally like VAT does.