I may not have quoted the CAFA, but I stated the sections so if you wanted you could look it up yourself.
"Section 39
(3) The local authority must secure that the EHC plan names the school or other institution specified in the request, unless subsection(4)applies.
(4) This subsection applies where—
(a) the school or other institution requested is unsuitable for the age, ability, aptitude or special educational needs of the child or young person concerned, or
(b)the attendance of the child or young person at the requested school or other institution would be incompatible with—
(i)the provision of efficient education for others, or
(ii)the efficient use of resources.
(5) Where subsection(4)applies, the local authority must secure that the plan—
(a)names a school or other institution which the local authority thinks would be appropriate for the child or young person, or
(b)specifies the type of school or other institution which the local authority thinks would be appropriate for the child or young person."
Section 33(2) which you quoted specifically opens with "In a case within section 39(5) or 40(2)". i.e. where one of Section 39(4) applies. You may have dismissed it in one of my links, but IPSEA state this about section 33 "If a parent of a child, or young person, wants that child or young person to attend a mainstream setting, the LA can only refuse if a mainstream placement would be incompatible with the efficient education of others, and there are no reasonable steps the LA could take to avoid this (section 33 CAFA 2014). The degree or complexity of their needs or disabilities, and the suitability of mainstream, is not a reason in law for refusal of mainstream. This applies not just to attending a mainstream school or college but also to taking mainstream courses.
This is an important right. The LA cannot send a child or young person to a special school when it is not what parents or the young person wants. This is true even if the LA view is supported by professionals.
It is important to note, however, that this is a right to mainstream education but not necessarily a right to a particular mainstream school."
As I said if your interpretation is correct you best inform IPSEA, and the barristers who write the SEN guide, as well as Judge Jacobs who ruled on ME v London Borough of Southwark (SEN): [2017] UKUT 73 (AAC).
No doubt you will write this off as 'only' a summary again despite IPSEA and the SEN noddy guide being well respected sources, but this page shows relevant case law.
"Judge Jacobs was clear that the wording in SS.33 and 39 shows the s.39 should be considered first and s.33 only applied if the LA does not access to the parents' request for mainstream under a.39. Therefore, a school rejected under s.39 may still be appropriate under s.33.
Basically what I have been posting, albeit more succeintly.
And this extract is taken from ME v London Borough of Southwark (SEN): [2017] UKUT 73 (AAC) directly (which IPSEA link to if you wish to read):
^"Section 39
- If the parents want their child to attend a specific school, whether mainstream or not, section 39 applies. The local authority must accede to their request unless one or both of two conditions are satisfied (section 39(3)). One is that the school is unsuitable (section 39(4)(a)). The other is that it would be incompatible with the efficient education of others or with the efficient use of resources (section 39(4)(b). If the local authority does not have to accede to the parents’ request, it must identify a school or type of school that is appropriate for the child (section 39(5)). The issue then has to be considered further under section 33."^
Just to reiterate this is not my interpretation of the law, but IPSEA and SEN barristers.
In the example of the hearing loop, as used in the SEN noddy guide, it explicitly states at that point there is no right to have a particular MS named, only to have it considered along with other schools put forward by the parent and LA with it already being shown one of the the disqualifiers in EA1996 s27 para 3(3) (which aligns with section 39(4) CAFA 2014) applies.