How well does he sit still?
I helped out with reception for a while. There was a kid who just wasn't interested in reading. It totally depended on his mood as to what he did.
Some days, or after a bit of bargaining he would concentrate long enough to show he could do it if he wanted to put his mind to it.
Most days though, he'd rather wander off and just didn't even try. He'd just make up anything and giggle. He was a bloody nightmare. It was clear he wasn't stupid and could do it - he just didn't want to on demand.
He was frustrating because he could do it occasionally if he tried. He just didn't want to.
He really really wasn't ready. And tbh I think one of the major issues was that the books for phonics are just so dull and shit.
On days you got his attention he would engage. The phonics books just weren't engaging. They were a chore. They are bloody awful books.
So I would absolutely stress finding books which are engaging and reading though with your son - and remembering how utterly dry and unengaging the phonics books are. I think there are certain kids they really don't suit and you have to find an alternative way into getting them wanting to read and finding reading fun forgetting about the formalities. Get the right book and they will engage more and eventually get it.
I think the issue with the testing comes down to this - it can be hard to tell who is struggling and who isn't engaging purely from the screening. It only tells you part of the story. If you have a child who does engage and is seeming to try but struggling that's an entirely different prospect to one who just doesn't want to sit with you and try and read. I think the kids that try but don't progress at all are more concerning than the ones who just aren't interested.
I recommend the 'My Bum' books for reception kids that won't engage. There's nothing like a fart jokes to get attention!
DS wasn't as bad as this, but he certainly wasn't the best reader in reception. We got him into books with comic books cos he hated everything they had in school. Even the none phonics books. Dogman helped him a huge amount and I know it was a game changer for a few of his peers in yr1/yr2. There's quite a few more options for younger kids now too than there were even a couple of years ago. Taking DS to a bookshop and letting him pick something suitable himself was also something that helped because it almost made him invested in the book from the start. (Library didn't work for us unfortunately - various reasons including not liking the look of the books in the library but finding the book shop ones interesting - the 'good' library books never seemed to be available so if he couldn't get what he wanted he sulked.)
I don't think it's a disaster but keep on top of it and keep trying. I found that having the kids read to me was interesting. They'd struggle and not get it until one day it just clicked and suddenly they were off and there was a lightbulb moment. That moment is fab btw. Especially if they have struggled.