Here are some suggestions.
Schools have a statutory obligation to report end of key stage levels ie end of year 2 & year 6. There is no legal requirement for them to report levels at any other time.
Some parents get outrageously competitive about the levels their children are achieving, in the way that some are obsessed about book bands in reception/year 1, so it becomes the talk of the playground.
I am very happy for my top English group in year 4 to know their levels; in fact they are motivated by knowing what progress they've made. However, my bottom maths set is a completely different issue. No matter how many times I say that our focus is on progress and how much they've improved, how demoralising would it be for a hard working child to hear they are, say, a 2a when their best friend who doesn't really have to try in maths is already a 4a?
A less able (or later to develop) child may well have still made significant progress, but for them that is moving up a sub-level as opposed to the 2 or 3 sub-levels that some children achieve in a year.
Children's progress is not linear - they tend to spurt and then plateau. This means it will often look like a child made loads of progress with last year's teacher and then very little this year. No matter how much I explain that's normal child development, a certain group of parents will start spreading it round the playground that I'm a crap teacher. Especially when they reach the end of the plateau and then spurt again next year.
Sometimes a child can be just into a sub level ie 3b and then 6 months later be a very secure 3b, just not quite a 3a. They've actually made almost 2 sub levels of progress, but it looks like they've made no progress.
Even with APP, assessments, careful marking of classroom work, observations of children etc etc etc, leveling is by its very nature subjective. I tend to mark my English group quite harshly because I know they can take it and it will do them good in the long run. Another teacher using the same evidence might be more generous.
We are in a system where the effectiveness of teachers is judged by the progress their children make. In my school there is no effective moderation of the levels awarded to children (that's a whole other debate...) so weaker teachers are known to be generous in the levels they award children so it looks like they've made good progress. That makes it incredibly difficult for the teacher the following year to show any progress at all, even though they know the child has progressed. Even when the management style doesn't encourage this sort of practise, some teachers (less experienced, those who've made a big change of year group) will find it harder to level accurately than others (done 10 years in the same year group and know in their sleep what a 3b looks like). This can lead to the same problem. Add to that the recent Government proposals that teachers' salaries will be determined by the levels their children achieved....
I'm not saying any of this to defend a system where parents aren't told the level their children are at. However, if a school has had bad experiences in the past (especially how parents use the information), I'm not surprised they've made a decision to not give out levels.
As I said above, at parents' evening I gave out the levels and targets for my English group but not my maths group. Any parent who asks me is told the level their child is working at. However, does knowing a child's level actually tell you very much? The teacher should be telling you about their strengths, and above all what they have to master yet. It's all about next steps in learning - it is good practise that children know what they need to work on next. Ofsted are actively asking children what their targets are. Obviously parents should know the targets as well (in some form).