I can only speak from my experience (of just the one ds
): teachers can come along and give their more holistic experience 
Ds' old primary school cared about punctuation and grammar as well as ensuring basic numeracy 
CfE was introduced formally, iirc, in the P6 of ds' time at primary school - but actually nothing changed at his school as that was the way that they had always taught (partly because it had 60% of its school roll with English as an Additional Language and it was an exemplar of best practice in the way that they dealt with that, with team teaching their normal way of working). The only thing that changed for the negative was the school reports
- but as we had a good relationship with the school and ds was ding well, that wasn't an issue for us.
Ds was in the top group for Maths at primary school (the head teacher, whose interest was Maths, took them) and was then in the top set for Maths at school (they set by the September weekend) and didn't seem to have any problems nor did he make any comment about going back over the basics. Ditto with English (although they only set after the October Week). (He'd also been slow to read, only "getting" it at the end of P2 but by the end of P4 was free reading and happily back in the top group for language).
He even missed a period each of English and Maths every week in S1 and S2 because he was in the "school of rugby class" and coped.
Iirc, he did complain about French as they did have to start again from scratch as one of the feeder primaries in particular was so poor in its foundation of the French basics. But everyone was in the same boat for Spanish.
I was a pretty hands off parent at secondary school though as he just got on with his homework, so I don't know much detail. I do recall him asking me for help on some Shakespeare (I think it was "Midsummer's Night Dream") in S1 as that was quite a jump for him - but that was probably because his very scary and intense English teacher was pushing them hard as she said it was a very talented cohort who were already working at Standard Grade level 
I remember my brother, whose kids are much younger than ds, complaining about things that their primary school said that they could/couldn't do because of CfE and I knew that it was just bad teaching practice as CfE said nothing of the sort
(as I was on the Parent Council at the primary school, I'd gone to a few seminars/workshops on the introduction of CfE as well as the school's own presentation).