My misunderstanding, I thought you were referring to the house wall.
One other point though, you talk of it not really mattering about how strong the wall is… you are very wrong on that point.
The footings/foundation of the wall is quite critical ESPECIALLY when you increase the height.
Your house walls for eg is basically a square box, the walls connect to and support each other, your fence wall is a straight line with no side walls to support it. It would normally have quite large and deep concrete footings to counter balance wind load for eg.
You say it’s only 40cm or so but I suggest that you lay on your back on the ground and ask your wife to drop a brick from 40cm above your head, and then repeat the experiment from the maximum height of your proposed wall…
In all seriousness imagine if your wall collapsed onto your wife or children or even worse someone else’s child ?