That's like saying the purpose of a blade is to cut, which while true, is a fairly useless statement. A blade may be an artisan's tool, or a soldier's weapon, or something you use to cut your food. All cutting implements but with quite different applications and functions.

So the question regarding the wall's function is what was it a barrier against? When we build houses, we put holes in the walls so that they are less of a barrier to people, yet remain an effective barrier against the external environment. Other walls are meant to be barriers to specific animals, yet completely permeable to others.

And it goes on to explain why that's not so straightforward:

"Contrary to the traditional view of such walls as solely defensive structures, the research highlights the Gobi Wall's multifunctional role in boundary demarcation, resource management, and the consolidation of imperial control."

Barriers can have different purposes though. e.g. One wall might be built because the people on one side want nothing to do with the other. Another might be built because the people on both sides are in a close economic relationship, but somebody else entirely wants to funnel that through choke points where intercourse can be taxed, monitored for information, etc..

https://en.wikipedia.org/wiki/Vietnam_Veterans_Memorial is a wall, but not really intended to be a barrier.

Okay, so what's the Western Wall in Jerusalem for?

wall(8) (previously invoked from /bin) is a Unix command to "write all", and wall used to emit a humorous error message, which IIRC was output when you provided no text to send as a message:

  But what do you want to do with the wall?

And I believe this was, in turn, a reference to adventure games like Infocom's, where the parser may detect that you typed a recognized noun without a verb in front, like "hit wall" or "push wall" and give exactly the same message as a prompt to include a verb.

Walls are just as commonly used as borders. Want your neighbour to not nick your land? Put up a wall. Make it heavy and a pain in the ass to move.

"The Gobi Wall was not just a barrier—it was a dynamic mechanism for governing movement, trade, and territorial control in a challenging environment."