When Augustus took the throne he made some rather big policy decisions that ended up sticking around. Among these decisions was the choice to stop expanding. Augustus realized what all the coming Emperors would realize- Rome was big enough.
This picture is Rome at its peak. The areas in bright red are the areas Rome wanted but that was it- it wanted nothing else. I am going to break down why Rome stopped where it stopped. If you want to only know about Africa, scroll down.
New territory means new resources but it also now means you have to station legions there, administer the area, and enact Roman authority. This is very hard to do in a time before instant communications. Say an Emperor passed a new law or ordered 1 Legion to head North. Well, that would mean a guy on horseback has to ride from Rome to wherever and show that order. Maybe that Legion can’t move because a barbarian Army is nearby. Well then that dude on horseback has to return to Rome with that info, see what the Emperor wants to do, and then return to the Legion. An Emperor ordering around a single Legion is unlikely to happen but you get my point. It took a long time to relay even basic information.
Augustus decided Rome was big enough- except for Germany, he wanted Germany. The Germans were dangerous, hostile, and right there on the border. If conquered it would eliminate a rather large threat and make Rome “whole”. The Germanic invasion went well, then it collapsed, and Germany would forever remain independent. Various German tribes and Roman Legions would clash again and again for centuries.
When Claudius took the throne he conquered Britannia. There were some really valuable resources there and by the late Empire Brittania was one of the most defended Provinces in all of the Empire. Now Claudius did this to associate himself with Caesar, following in Caesar's footsteps so to speak. While Brittania fell relatively easily conquering modern Scotland became a nightmare. The mountains were hard to word around and the people there were very warlike. So while Rome did kinda conquer part of Scotland for a while, these conquests were eventually abandoned.
Then we have the Middle East. This area was home to the Parthian Empire- Rome’s longtime rival. The two Empires had gone back and forth for years and every great Emperor had the ambition of defeating Parthia. In the end, Trajan would conquer a good chunk of Eastern Parthia (modern Iraq basically) but be prevented from going further by the terrain and his own death. Holding onto this region was very difficult because it was a long way away from Rome and the Parthians out East (in Iran) wanted it back. So when Trajan died Emperor Hadrian traded this region back to Parthia in exchange for a lasting peace (which did not actually last).
Now we have Africa
The Romans conquered Northern Africa way back in the days of the Republic. In the early days of the Roman Republic Northern Africa was part of the Carthaginian Empire. In the 3rd Punic War Rome would conquer Northern Africa (and what remained of Carthage) and begin to administer this region. It was a central grain production site and a crucial trade city. Rome also allied with various Kingdoms in Northern Africa and eventually just absorbed them into the Empire as a whole.
So why not go further into the rest of Africa? The Sahara desert. This Sahara is not small- it’s actually insanely large.
Imagine crossing this desert. Rome would need to send entire legions through it. How could you keep those legions supplied with food and water? It’s very hard for experienced locals to navigate the desert- what are the Legions going to do?
As I said Rome had a hard time managing Legions in modern Scotland or Iraq- and these areas were not inaccessible by any means, they were just far away from Rome. If they struggled with Iraq how would they do with Southern Africa?
Is it possible? Maybe. Maybe Rome could have moved down the Nile river but that is about it. The expense of such a venture though is insane and the juice is just not worth the squeeze.
Rome had all the resources it needed, and it was already too large. Trying to take a desert the size of the US and then occupy a massive continent would be nearly impossible, extremely expensive, and likely would not bear much fruit.