Hadrian and Antoninus Pius built their walls in an effort to subdue the barbarians actually. They both built the walls in the middle of territory controlled by Pictish tribes, meaning they essentially severed the enemy in half, cutting resources, movement and communication between the disparate tribes.
The walls also served to control (and tax!) commerce, which is much more profitable long term. Rome’s borders were inconceivably porous to the modern mind. Roman citizens often lived far beyond the official boundaries of the empire and many client states and tribes operated within its borders with varying levels of freedom
Finally, it just wasn’t worth the money or manpower. Look at the eastern border. Between Trajan and Constantine, it had almost become an imperial tradition to march all the way to Ctestiphon, capital of the Persian Empires, and sack it. Occupying and controlling the territory served no economic or strategic benefit and the people of the region were often rebellious. In Britannia, the Romans already controlled all the major mineral resources of the island, and as you go further north, Britannia becomes more mountainous and swampy, both miserable to campaign in, let alone control. And, if we look to Hadrian’s Dacian conquest, we see miserable territory that was determined to be worth the risk, due in part to the massive gold mines found in Dacia.
On top of this, Hadrian had instituted a major shift in Roman military policy and posture that further demonstrates that it wasn’t worth the manpower, shifting the Roman military into a defensive force.
Oh, also, any real existential threat to Roman supremacy had already been dealt with and driven into the ground. What remained were raiders and insurgents. It wasn’t anything like the migration era hordes on the Rhine and Danube frontiers.
So, to conclude, the walls existed to really muck up opposition from Pictish tribes in Britannia while also controlling and taxing trade. The territory was demonstrably not worth conquering, and Roman military policy had shifted to not even really caring too much about new land, especially land as relatively useless as modern Scotland.
Hey there,
Just to let you know, your question is fine, and we're letting it stand. However, you should be aware that questions framed as 'Why didn't X do Y' relatively often don't get an answer that meets our standards (in our experience as moderators). There are a few reasons for this. Firstly, it often can be difficult to prove the counterfactual: historians know much more about what happened than what might have happened. Secondly, 'why didn't X do Y' questions are sometimes phrased in an ahistorical way. It's worth remembering that people in the past couldn't see into the future, and they generally didn't have all the information we now have about their situations; things that look obvious now didn't necessarily look that way at the time.
If you end up not getting a response after a day or two, consider asking a new question focusing instead on why what happened did happen (rather than why what didn't happen didn't happen) - this kind of question is more likely to get a response in our experience. Hope this helps!