Registration for children in your child's circumstances (born outside the UK to parents neither of whom were British citizens at the time of the child's birth) is already at discretion, under Section 3(1).
But discretion does not mean the absence of rules or requirements. It merely means that the Home Office can lay out the expectations of when that discretion will be exercised.
Currently, the expectations listed in
the guidance are
(a) lived in the UK for 10 years lawfully (on any combination of visas, does not require ILR), or,
(b) at least one parent has or is applying for British citizenship, and both the other parent and the child have ILR.
You would need to give compelling compassionate reasons why a child not meeting these expectations should be registered as a British citizen if the conditions above are not met. And saving money is not a compelling compassionate reason.
So, to summarise, children in these circumstances do not have an entitlement to British citizenship anyway and meeting the requirements above is for the Home Office to exercise discretion.
I am not a lawyer or immigration advisor. My statements/comments do not constitute legal advice. E&OE. Please do not PM me for advice.