I think the text is pretty clear and unambiguous.
The heartstone enables the pre-existing etherealness ability of a Hag. If you are not a hag, the heartstone does not do this for you.
The touch of a heartstone cures any disease. There is no limitation on who might be holding the heartstone or how many prior times it has been used in this way.
So, based on this, RAW, if the PCs obtain a heartstone, they can cure any disease at-will, and an unlimited number of times.
The consequences, however, could be very interesting and subtle and long-term. Nighthags, for example, as fiends, are not permanently destroyed when killed on the prime material plane - they go back to their home plane and reform. They will probably want their heartstone back (grudge-match). Now, the party could do shady stuff like take that heartstone and cure only the diseases of the rich who would pay an hefty price. Might this begin to corrupt some or all of the party? hmmm...maybe. Might Hag then regret less or not at all the loss of her heartstone? Definitely maybe not.
On the other hand, imagine a nighthag is slain by an Oath of Devotion Paladin, and that paladin now takes that heartstone and goes from town-to-town curing every disease in sight - every disease - for free. That hag would be pissed - not only did they loose to a goodie-goodie, that goodie-goodie is now going around and eliminating disease. The plots and hard work of all the bad guys might suddenly get unraveled. The hag might get a phone call from her superior saying "This is your fault. You have one chance, and one chance only, to fix the situation. You don't want to know the consequences of failure". So the hag calls in some favors, gathers a possie, and big-time-grudge-match is on! Or, maybe if the afore-mentioned paladin repeatedly empties the disease ward of every hospital in an area often and in a sustained way, the doctors might pack up an move (ie: "guess we are not needed here"), the city sanitation practices cease (if there are no consequences for disease, why bother with prevention) - local healthcare becomes dependent on the traveling dude with the cure-disease-free stone. Then when Pally leaves for a while - oh boy - plague city. What would the Pally think of that as consequences for their well-intentioned actions?
Yep siree. Gold. Absolute plot gold. Far from breaking the game, it can make it 10x as interesting.