It should be noted that medieval kingdoms didn't have capitals that functioned exactly like they do in the modern world. While London or Paris would have been the center of commerce and would have been the places listed if you asked someone from the time what the capital of the country was, the actual king and his court wasn't necessarily to be found in those cities. In England specifically, due to some very complicated reasons that go back so far that we don't even know when they began, London functioned (still does, to an extent in fact) as a sort of independent city-state within England and the kings were always worried about its power and influence. If you look at a map of the official City of London (which is actually a different entity from London for the same complicated reasons) all of the castles and palaces owned by the royal family such as the Tower of London are actually outside of the official boundaries of the city. Regardless of this, the court also didn't usually stay in one place for long anyway. Due to the logistics of feeding hundreds of nobles who would have demanded meat and other luxury food, the desire to escape heat in the summer and cold in the winter, the need to travel long distances to deal with regional issues and the only way to escape plagues being to move away from population centers, the king and his court would usually only stay in one castle for a few months before moving to another one.

"Why not" is always going to be hard to prove, but there are a couple of points to be shared on the subject. In his rather enjoyable work "The Heart of Europe", Peter Wilson gives some reasons that no significant capital developed for the Empire as whole.

While some cities held special importance due to their symbolism. such as Aachen, the early years of the Empire followed an itinerant policy as opposed to developing a strong centralized bureaucracy which might've been outside of their grasp at the time.

Save for some periods in its history, the Empire seemed to avoid centralization efforts from its Emperors. Wilson makes the argument that this was not to its detriment, but instead allowed for strong development within the lands of the "autonomous" princes of the Empire.

He notes that the more decentralized, or Territorial, the Empire became, the more it required a dynasty's personal wealth to run. As the Imperial office pawned off more and more of its resources, the more it required the emperor himself to have substantial holdings to cover his own cost.

Obviously this would narrow down the possibility of election to a few rich players.
The Kingdom of Bohemia produced some of the Emperors during this period, and their substantial wealth allowed them to develop Prague into a major city of its time. This included creating the first university of Central Europe within the city.

Later on, the Habsburgs famously gained a virtual monopoly of the Imperial title. During this time, Vienna would be seen as their dynastic capital.

So while the empire itself was not known for giving official primacy to one of its kingdoms, the dynasty in control of the office could choose where they would operate from.

Again, the book by Peter H Wilson has a great breakdown and argument for the benefits of the territorial manner of the mid to late HRE.