Like most taxes, once a government gets them in place, they are reluctant to lose them. A trade off would be to transfer the payment from the buyer to the seller.
Inevitably at the point of purchasing a house, the buyers finances are stretched. The additional tax at this time is throttling the market partticularly for first time buyers. Especially at a time of high deposits.
Sellers who go on to become buyers remain tax neutral if both property values are equal. People trading up still pay tax at the lesser rate for the sold house, so do not need to find extra funds, again at a time of financial strain. Sellers moving out of the market or trading down, will pay the tax at the top of the chain. These people we would assume are in a finacially strong position with cash in the bank. At this point it is less difficult to find the funds.
In the early days there may need to be some sort or staged transfer of responsibility from buyers to sellers to avoid situations where people are unfairly treated by having to pay twice, if they are leaving the market within a couple of years of buying.
Why is this idea important?
This would help stimulate sales, especially for first time buyers, Instead of finding a lump of cash when they can least afford it, the seller will pick up the bill.
Inevitably, the builders of new properties will want to recoupe the duty by increasing the price of property, so the market values will be forced up. The buyer will however only pay a slightly larger deposit for his mortgage.
Overall it will stimulate the housing market.