Registration as British Citizen or Indefinite Leave to Remain?

I'm an Australian citizen who has worked in the UK for 5 years on a Tier 2 General visa. I'm about to apply for Indefinite Leave to Remain (ILR) for myself and my two dependent children associated with my visa. After reading about applying for citizenship I thought I might be able to skip the ILR for my children and register them as a Bristish Citizen?
This may?? be possible as my wife, who is also an Australian citizen, came to the UK at the same time using a Certificate of Entitlement to the Right of Abode. Since arriving in the UK she has become a British Citizen and now holds both a British and Australian passport. To complicate matters we have recently separated but both intend to remain in the UK and she would support any application.

Children born in the UK are entitled to register as British citizen if at least one parent is granted settlement (ILR or Citizenship).
Children born abroad can be registered too but they are expected to have ILR, along with both parents and it is also expected that at least one parent is or is applying to become a British. However these expectations can be set aside and the child can still be registered if you can make a compelling case (e.g. if both parents are British)
Applications for such children (born abroad) is an application at discretion, not an entitlement/right.

Thank you! Yes, that makes sense. I don't have ILR yet so I think for certainity we'll just all apply for ILR.