I think LA funded placements at private schools for SEND/ALN pupils varies massively in different parts of the UK. England and Wales have two completely different approaches to this.
Whereas it seems to me that English LAs will very often fund (or be forced to by Tribunal) these private placements, it is vanishingly rare in Wales. This is impacted by many factors, but I think one of the main ones is that state schools in Wales are LA maintained (even the Voluntary Schools e.g Church in Wales, are LA funded). There is a very strong political preference in Wales for community comprehensive schools, many of which have attached 'Units' for more severely disabled children who cannot attend mainstream. Kids with less profound ALN/SEND are expected to attend mainstream with varying levels of support. This is obviously different from school to school and county to county, and is very hit and miss, however the presumption is that children will attend LA maintained schools (including Specialist ALN schools, but there are too few of these to meet need), rather than fund private provision. Obviously there are exceptions to the rule, but these are very rare. Wales also has relatively few private schools, particularily outside urban areas, and no Welsh medium private schools. Only 2%ish of children in Wales attend private schools (the rate being much higher the closer you get to England e.g. Monmouthshire with 12%) compared to 6-7% of English pupils. I think that the Scottish rate is around 4%ish with N.I. less than 1%. Interestingly, N.I. pupils have the best academic performance of the four home nations (https://www.nuffieldfoundation.org/news/new-study-compares-pupil-performance-across-uk-nations ).
This summary from a NASUWT report earlier this year shows where some of the challenges are in the English state system:
"Key Findings: Where Is the Money Going?
Academy Trust CEO salaries are soaring – Some chief executives are earning over £500,000, far exceeding the Prime Minister’s salary.
Consultancy spending is skyrocketing – Academy Trusts spent £412 million on consultants in 2022-23, nearly double the amount five years ago.
Profiteering in SEND provision – Private SEND schools are charging up to £61,500 per pupil, compared to £23,900 in state-funded schools, with some companies making tens of millions in profit.
Supply teacher agencies cashing in – Schools spent £1.2 billion on supply teachers in 2022-23, with agencies pocketing £300 million in fees.
Councils crippled by SEND bill – As councils struggle to provide provision they are increasingly forced to turn to the private sector. Calderdale Council saw spending rise a 477% in four years, from £699,409 in 2020-21 to £4,035,607 in 2023-24."
So @Isitbetterb, what I think you also need to take into consideration is the provision of the home nation you reside in. We realised that moving between them was not such an easy proposition when considering language, culture and political aspects of education in the various nations.
In reality, the question is much broader than simply state or private.