Having worked in Y2, Y2/3 and also in upper KS2, I have had the chance to do a LOT of moderation of L3 work. At our school, we focus more on the sentence structure of children as this seems to us to be the best indicator of a secure L3. I think people are often keen to award L3 when faced with a few elements of a couple of L3 AFs eg attempts at speech marks or paragraphing in what is otherwise a very basic piece of writing. A variety in sentence structures and a range of connectives stretching a bit further than and/but/because prove more useful indicators for us. So being unable to use paragraphs might be quite a minor feature if the child was using some complex sentences.