What was the point of Griphook demanding the Sword of Gryffindor? Since it can "present itself" to any worthy Gryffindor, he has no way of compelling it to stay with him. So what exactly can he do with it?
Related, particularly Valorum's answer: scifi.stackexchange.com/q/60724/76048– F1KrazyMay 5, 2022 at 13:56
One could argue that a Gryffindor that would try to take the sword from its (new) rightful owner is not worthy.– chepnerMay 5, 2022 at 16:34
Depending on the spell used on the sword, it may be possible to use some sort of counter-enchantment in order to prevent it from disappearing, or work out some way to block it from transporting to Gryffindor's hat when requested.
Having unlimited physical access to the object would, presumably, be advantageous to anyone who wants to perform a lengthy spell or work out how to use this powerful magical object by trial-and-error.
As to why they wanted it, the simplest answer is that he considered it to belong to the Goblins by right.