It's too easy to think of a wall as defensive, because 99.9% of the time, they're built to defend something. Take for example a city wall.
This has the effect of levelling the odds between a weaker force (in the city) and a strong force (outside the city).
Now take Hadrian's Wall. In this case, the stronger force is inside (the Roman army) and the weaker force outside (the various northern Celtic tribes). Would the Romans want to even those odds? Of course not. The practicality of this is that if the Romans were to fight ('defend') the Celts from the top of a wall, they can't bring into play their greatest strength, which is the ability to fight in huge numbers in carefully drilled ranks from behind a shield wall in the open. . . with Cavalry to keep the edges tidy. No matter how many legions you have south of the wall, you can only fit a couple of infantrymen or so, per metre of wall, and the Cavalry are useless.
This is why the forts were moved to the wall line from the Staingate (about a mile to the south), and in many case built astride (rather than abutting) the wall. With six gates to the north of the wall, they could get large numbers of troops and cavalry into enemy territory very quickly.
There's also no hard evidence of a walkway existing atop Hadrian's Wall, and many scholars have argued that it didn't exist, for just the above reasons.