I’d check other sources. Everything that I read about Hadrian’s wall (and I’ve only done that since I saw this post, although I “knew about” the wall without having done any particular research until just now) indicates that there were “mileforts” spaced approximately a mile apart along the wall, each of which was garrisoned with 60–100 legionnaires. Between the mileforts were lookout / signal towers, spaced roughly at ⅓ mile intervals. Spacing was approximate, to take advantage of (or avoid) local terrain features.
Yes, there were “major” forts (and gates) at roughly 14-mile intervals, but I can’t imagine that there would be any need to space them with concern to whether the troops from another major fort could reach them with a half-day’s march. Considering the cost to build the wall itself (and its accompanying defenses, which were fairly extensive) and garrison the mileforts and signal towers, even the Romans must have had economic considerations about not only building but then staffing and supporting additional forts (and gates).
To my mind, one of the most significant concerns would have been that those major forts were the locations of the gates in the wall. In other words, the wall’s “major fortification” is also its most vulnerable point if the troops do march out to another fort. So, when they build another major fort, then they need to add the cost of maintaining another 1000 or so legionnaires, and that’s a considerable cost to any frontier army.