Norah
It wasn't the Duke who donated money to the NHS, it was the Westminster Foundation which is a registered charity set up in 1974. This would have been funded by the various family trusts or members of the family personally. It's possible that the charity receives some government funding for some of its work.
As well as cash, property, land and shares can be given to a charity and there is tax relief available for such gifts.
I'm sure that you are aware that in the UK the threshold for paying inheritance tax is £325,000. Above that threshold the rate of tax payable on estates is 40%. There are many reliefs available to taxpayers, such as if your home is left to your children. In that case, provided that your estate is worth £2million or less, the threshold will increase to £500,000.
The fact is the Grosvenors and others like them (such as the Vestey family) pay no where near as much tax as is paid by most of the population.
You ask if the Duke's assets were taxed how would that benefit anyone else? I'm not talking about a wealth tax but the avoidance of tax (perfectly legal) on assets by the transfer of those assets into trusts. Included in the various trusts would be the properties occupied by members of the Grosvenor family. Once held by a trust the assets do not belong to the individual. Trusts are for the benefit of future generations, to keep wealth within the family.
On the death of his father the present duke inherited £9.6 billion. That represents rather a lot of tax not benefiting the country.
The treatment of trusts and charities is highly complicated and my response is necessarily short and simplistic.