Now, if there was a clause that stated that income from the Royal estates was to be used to fund, for instance, the NHS, then your statement about the public purse may be true. As it happens though, it is misleading because that income is used ...

"entirely to support The Queen’s work as Head of State.

Dave, you may wish to re-read it.
I read it that the 15% (or 25%) goes to cover those purposes (i.e. entirely to support The Queen's work), the remaining 75% or 85% goes to the Treasury (i.e. us) and becomes part of the general fund which does cover government spending, including the NHS.