It’s not as simple as that. In a primary, for example, the budget is predicated on 30 children per class. So if a class of 25 gains 5 more pupils, that is pure financial gain.
Yes, if a school is 30 children short per year group, then 1 teacher can be saved - but that’s really quite rare. What’s much more common is being 5, 10, 15 short, and so those extra children are pure gain.
Resources etc -particularly consumable resources such as paper - are MUCH less costly for a school than the fixed costs of classrooms and the almost-fixed cost of teachers.
TAs are a moot point. Given that the children of privileged families who might previously have gone private are not likely to disproportionately feature very high needs children, then a simple change in numbers is unlikely to affect TA numbers that much. Many schools now only have 1:1 TAs for high needs children anyway.
The staffing of secondary schools is more complicated, but in many ways the same principle applies - if 5 children likely to take MFL join, bringing the GCSE MFL class to 28 from 23, that’s more money in for none out. Yes, in some cases a school may be able to cease offering a subject or drop a core subject teacher to part time if they shrink in size, but for that has to be offset every class that moves further away from an economic size as numbers decrease.
Yes, in the same way as the private schools that have announced closure are often smaller, or operating well below capacity, there may be some savings available from closing a few state schools (as happens every year) but saying that ‘keeping private schools open is a financial benefit because some state schools can close’ is not a clear cause and effect relationship.