No, in most countries the stamp duty remains. I thibk i paid 3.5% here.
A 1-2% property tax may well be double or triple your council tax, but so what? That largely means the council tax was probably insufficient. For a property tax to have a measured impact on house pricing it has to be hugh enough that the tax acts as an incentive to moderate house buying.
If the property tax is not affordable then you either have to downsize or rent. E.g. here, rental costs are abput 2-3% tops, while a 1.5% property tax and 2-3% or more mortgage means it is much cheaper to rent than buy. As long as there is proper rental controls in place and strict protection for renters then there is zero problem with renting. Buying is a strangly British obsession
If you rent and it's same cost as mortgage. How do you afford your retirement when pensions basically evaporate?