Where I'm from, the school leaving age was also 16, and it was the student's choice to leave, as it always is - our main exams weren't til 18 anyway. Those who are sensible and value education are going to stay; those who aren't, a few months isn't going to make much of a difference - if they're not on course for passing GCSEs already and are wanting to leave, chances are that being forced to stay isn't going to help either.
And kudos for being able to e.g., drive earlier might help offset it.
When it becomes an established possibility, the novelty wears off and people just become used to the idea that people of different ages can be in one year, and it really doesn't make much difference to peers. School admissions don't tend to be that affected either, as it all balances out. People aren't desperate to defer just for their child to be oldest - they do it because they feel a need for it. Nobody wants a child who is unmotivated and bored from being too old, either, and they realise that it wouldn't be in the child's best interest to defer if they are otherwise ready. It just doesn't became a huge issue. The majority go in at the correct age. A small number defer. A few end up repeating or skipping years.
But children are on average half a year older there when they start than they are here, because of the Mar-Feb cut off dates for normal admissions. And the first year is very gentle (half days) as well.