There is a general misconception that a good wall keeps out the barbarians. Unfortunately, history has proven time and time again, that those that believe a wall, in and of itself, can stop an impenetrable force, or stop devious designs, or stop those that are fiercely determined, or stopped those that will not be stopped, has been proven to be wrong, countless times.
The biggest problem with a wall is the fact that it is stagnant, and a stagnant barrier is a barrier that anyone with any sort of sensibility can spend an inordinate amount of time, trying to come up with plans that will overcome that barrier, in one manner or another. For instance, any wall can possibly be breached, by going around it, tunneling underneath it, or by going over it. Further to the point, even the most impenetrable barrier, should such actually exist, can still be breached, if those that guard that wall, or have constructed that wall, or know intimately of that wall, are compromised in a manner in which, solid, actionable information is passed on to another, for those others to then take advantage of in one form or another, for many a wall has come down not truly from without, but truly from within.
While walls and doors have their place, the fact of the matter is that a wall or door will give ground to a force that is concentrated and powerful. So too, a wall will give ground to those that are aware of its weaknesses, and soft points, and so on and so forth. The purpose of a wall, whether it be at a border of a country, or to demarcate exclusive neighborhood housing, is more to be seen as the marking of territory, and the semblance of a defensive structure to protect and secure countries and neighborhoods, but to absolutely secure such, necessitates far more than any wall can provide, which would also commonly entail intelligence, materials, manpower, equipment, and an overarching strategy. Even then, a superior or more devious force can still rather readily overcome any wall.
There was a time when forts had their value, and even today, forts have value, but the problem that a fort has is that most forts in one form or another, can ultimately be cut off from supply lines and once that is successfully accomplished, the writing is pretty much on the wall. So too, nations that are successful in cutting off all outside interference can only possible survive and thrive by being self sufficient in everything that they could possibly or conceivably need that they had previously procured or traded for outside of their self-imposed walls, and should some of those supplies thereupon be necessary for whatever reason or reasons, than their isolation will be breached, and from there, so too will their walls.
There aren't any impenetrable walls because there aren't any impenetrable defenses; so that, rather than believing that such a wall can and therefore should be constructed, it would be far better to spend time and resources creating the atmosphere and knowhow to deal with situations at a more dynamic and comprehensive level; rather than believing that a big, bad wall is going to stop much of anything.