OK. You have explained your thinking well. Yes, of course, real value and thus adjusted for inflation.
However. Let us assume the following scenario. Mum wants to leave one of the daughters her home once she departs. Mum thinks that remaining children can have the equal in shares and cash. She passed on happily convinced all is well. Then daughter subsequently finds out, on her attempt to sell mum's property, that she has a tax bill as mum's home has beaten the CPI significantly over the years and still finds herself with a significant tax bill unanticipated by mum or herself and dependent on her marginal tax rate at the time of the sale. I can't see why this is a great alternative to a Death Duty charged on the entire estate and thus tax paid will be shared between all beneficiaries (effectively) because it becomes an overall tax, depending on the size of the estate in total.
Moreover, it is messy because mum may have downsized from the family home and thus this should become a tax credit passed on to her beneficiaries on death? This downsizing shouldn't be turned into a tax problem as it distorts the pricing system as people need to make decisions such as this without being concerned about tax implications being different because it's a downgrade rather than an upgrading. Too messy.
I see no reason why taxing the entire state as a death duty is not preferrable. It should have a tax-free status up to a certain level (and a generous one at that), and then be progressive beyond that. The family home should just be part of the total assets to be assessed for this tax.