Teaching an 11 year old to use a smart phone responsibly is relatively easy.
You can restrict where and when they use it
You can demand to see it on a regular basis
You can legitimately ban or restrict social media
You can have a system that restricts use and where a parent has to approve new apps.
The idea of doing that with a 16 year old... nightmare.
Most 15/16 year olds today have grown up with smart phones and social media and are far less interested in likes and follows than those who are now in their early 20s are. Restricting to 16 is likely to start that back up again.
There are so many uses for smart phones. DD uses it for travel - bus and train apps and tickets, contacting friends, homework apps, guitar tuning apps, music apps. It's a godsend.
I have a tracker on it - we live rurally and she has a long commute to school or to see friends at weekend. I can log on and check that she's at school, or when her train is likely to get in, or if she's made it to her friend's house without having to message her.
In any case the genie is out of the bottle.
What is far more likely is your child will end up with a hidden smartphone you know nothing about and have zero control over.