I understand the frustration, that being said, it's not that hard to correct. First, contrary to previous editions, in 5e, unless I'm mistaken, once applied, the poison stays on the blade for one minute, which is way longer than most fights, so there should not be a reason to reapply it.
As for applying it, for the sake of fairness, I would require NPCs like drows and assassins to use bonus action to apply it, with the assumption that they did it before combat in most cases. After that, find additional doses is another matter. Poison is not that balanced in the game, never has been whatever the edition, sop allowing too many doses of very potent poison for PCs is unbalancing the game, and I'm not sure that there is much that can be done about this.