There has been a lot of speculation about Hadrian's wall and what purpose it served but the truth is, we don't know. As you say, it was not a particularly imposing defensive structure. Too long by far to be effectively held against a determined attack. There are several possible theories on why it was built:

1. To control raiding and smuggling. Raiding and smuggling was common and while the wall could not defend against an army, it was a real obstacle for raiders and smugglers.
2. To control trade and taxation. Roman influence usually extended beyond the border too (similar, but not continuous, fortifications existed in Germany for example), the gates in the wall would have been an excellent place to collect taxes and tolls.
3. To show the power of Rome. The wall, while not remarkably tall, would probably have been white when it was built. Drawing a 117 km white line right across the country just to say "Here's the border" sends a pretty powerful message.

It may well have been a combination of all three reasons, or neither. As I said at first, we don't know. The roman border in Germany was built around the same time and lacks a continuous wall, relying instead on some ~60 proper forts and hundreds and hundreds of guard towers.

What I can tell you from a military point of view is that, as we understand the military of that era, it makes no sense to build a 73-mile wall. Given the troops available and the area around it would have made far more military sense to defend/control the area with a few more powerful forts and patrols.