"Following the letter of the law / statement would mean the child sitting one-to-one with the TA and no other children."
I think that depends on the individual statement wording and how you are interpreting it. A TA can work 1:1 supporting a child with SEN to interact with their peers - they are there 1:1 with the child to focus only on their needs, advise and support, There is unlikely to be anything in the wording to preclude them from interacting with the other pupils, just from supporting them.
In some cases however, even this would be a step too far for the child's needs. In those cases, the 1:1 work with the TA is required to build the skills the pupil will need in order to start working with other pupils or working more independently. It might be reciprocal conversation skills, listening skills, tolerance of others' opinions and ideas and those are just off the top of my head. The TA and the statemented child would therefore need to work on developing those skills, before taking them on the road and using them whilst interacting with peers.
Statements aren't set in stone for the life of the child's education, they are reviewed annually for a reason. If a child has, as per their statement, been supported to gradually learn the skills they need to start either working with other pupils or working independently (depending on what the individual needs) this will be noted at the Annual Review and changes made to move towards less 1:1.
Yes, statements can seem prescriptive, but as insanity pointed out, a statement that is specified to that extent has usually come out of a long process of assessment and consultation with professionals who are fully qualified to decide how much or little support a child needs 'at that point in their education'.
I understand teachers sometimes feel that statements are prescriptive/constrictive, but it's a simple fact that teachers in the UK are not trained in SEN to a level which would allow them to make judgements on the level of support required for many children with SEN.
As a parent of a child who has Autism and has a statement that is tightly specified, there is nothing worse that being told by a teacher that they know better than the extensive team of professionals and experts who have done in depth assessments and consultations to decide the best way forward for their needs.
My ds's teacher spent the whole of last year trying to tell me (and anyone else who would listen) that he isn't autistic, because of course she would know better than the experts that diagnosed him via a lengthy and complicated multi-disciplinary team assessment, in conjunction with the school, LEA Ed Psyche and ASD Inclusion Team. She was wrong, yet she saw fit to ignore his statement for the whole year, undoing much of the hard work his team had put in the year before. She felt he didn't need the level of support specified in his statement and as a result he lost skills and ended up with massive anxiety, which of course she failed to see - because she's neither qualified or trained to do so.