Can anyone confirm this to me, but wasn't a huge problem for the HRE that they never managed to have a stable succession?

It's difficult to answer a hypothetical, as to whether the HRE could have 'centralised' ala France or England, at least in the way we think of it.

I can only speak to the early modern HRE, after its medieval development, but the Habsburgs definitely had hopes that they could 'centralise' the HRE and the German Confederation that followed it. They never truly gave up their ambitions to truly unite Germany beneath their rule until the mid-19th century, when Bismarck and the Prussians truly ejected them from Germany, outside of their traditional hereditary lands.

Of course, we have to consider what we mean by 'centralisation'. I would presume that by centralised, you mean something like what happened with France or England/Great Britain where--while there were definitely domestic opponents of the monarch--the monarch and their royal bureaucracy controlled the machinery of state. I would also assume you mean that the central government must have its monopoly on the legitimate use of force that's the basic principle of the modern state.

So, could the HRE have become centralised in this sense? To give the attorney's answer: maybe.

At least partially, we have to consider that the HRE was based heavily on the elected nature of the Imperial title. If you wanted to be Emperor--or wanted your chosen successor to become Emperor after you--you would have to deal with the electors and the other Imperial estates. This would often involve confirming their rights and privileges before they would offer you their support in the Electoral College or Imperial Diet. For particular issues, you might have to offer new rights and privileges to a key elector or prince in order to get your election confirmed or your policy enacted. The Emperor could not rule simply by edict. His decisions would have to be accepted, not only by a majority of the diet--but due to the lack of any true 'imperial' bureaucracy--actual enforcement of whatever new policy would have to be left to the local princes or circles. While small scale princes, Imperial Free Cities, and others might just do as they are bid since they are dependent on the continued rule of law in the Emperor to protect themselves. However, the larger princes who could maintain their own armies could defy the Emperor, for which there may not be any recourse but the use of military force.

The Imperial Courts--while they did exist and are interesting--had their own issues. Cases could take many years to pass, and while they were good for maintaining the general rule of law in the Empire, but weren't well suited to deal with sudden crisis.

So, to wrap up, could the HRE have centralised--at least how I've defined it? It's hard to answer. There were definite issues present, tied heavily to the need for the Emperor to be elected and for consensus and agreement amongst the German estates that would be hard to overcome to turn the HRE into an early modern German empire.