There are several issues if children join a state school after Christmas 25 - the school will receive no funding for that pupil till September 26 (funding for 24/25 is based on pupil numbers in October 23 and for 25/26 on the census in October 24).
There is as much SEND in independent schools as state - more diagnosed, because parents more ability to fund private assessments and acknowledged by schools as they charge for the support.
House prices near good/outstanding schools will increase as those that can afford it will pay (already happens) particularly grammar areas.
There may be surplus spaces, many in London as school rolls fall as families leave London, but there are plenty of children/parents not getting their school preference, the places are often in the less desirable schools because they are not preferred.
Average class sizes at key stage 3 are around 32. Independent schools have between 16-25 at the same stage.
Not all deficit schools are under subscribed.
6500 teachers 1 split between 4 schools is not going to go far (approx 24,000 state schools in UK).
The wrap around care doesn't exist in the required amount now, many parents deciding on state/ unable to afford private, will need provision that is limited since the pandemic and the potential increase in numbers at primary in state, needs time to adjust (primary is most likely to be first impacted as parents decide to wait for secondary).
When this is introduced it needs to be fully funded as the change happens, but it could be a way of delaying impact on spending by allowing the census to catch up with funding.