The NSW govt (Australia) brought something in like this. It lasted 6 months and then the new govt repealed it.
You could elect to pay SD or pay the new annual charge. I'm not sure if it was always going to be a choice or whether it was during the transitional period you got the choice.
Anyway we chose to just pay the SD. The charge would be on the value of your land which of course goes up whether or not you improve your home, plus they could increase it by up to 0.x% (I forget the details) per year.
We would have broken even in 15 years assuming no increase in value of the land (impossible as it was a huge plot) and assuming the govt didn't raise rates (pigs, fly).
It seems like there are so many better things the govt could do to encourage people moving up and down the ladder, like giving the over 65s a ratcheting stamp duty discount if they replace their primary place of residence from a house to a flat, and/or with a new primary place of residence with fewer bedrooms, with the potential to get a bigger discount if you go from a four bed to a two bed than if you go from a four bed to a three. Am I being naive or would this not be easy to administer where conveyancers are involved as they are buying and selling your houses at the same time and knows exactly how many bedrooms they have).
(No of course I am not suggesting any older person should be forced to sell up but this may take the stamp duty sting away for those who would entertain the idea but bought their house for a song in the 70s and wouldn't mind a smaller place that's easier to heat and maintain but can't fathom paying thousands in stamp duty to downgrade).