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But it's a one off cost on each move; it doesn't have any capital value after spending it but it prevents people moving e.g. to downsize or because they can otherwise afford to upgrade.
Imo an annual roperty tax would be a better way to tax real estate - it wouldn't dissuade people from moving and would also have a chance at capturing the value obtained by people sitting on appreciated assets. Rather than loading the cost onto the purchaser (who is already going to be the one funding any capital gain made by people who've seen their properties increase in value).
If you've got £1m+ to drop, it seems a little petty to moan about the 4.4% purchasing tax.
Edit: and as someone who recently had to pay a large (not that ^ large admittedly) chunk of stamp duty, it seems to me to be a reasonable way to raise revenue.