This is "often appropriate"
The DMG Section on Using Ability Scores (p.237) says:
When a player wants to do something, it's often appropriate to let the attempt succeed without a roll or a reference to the character's ability scores. For example, a character doesn't normally need to make a Dexterity check to walk across an empty room or a Charisma check to order a mug of ale.
In your world, do the characters have to make Charisma (Persuasion) rolls every time they order a mug of ale? If not, then you are already choosing to make success automatic in some cases. In this particular case, because of all the "great effort, planning, [and] previous resolving" of the player, you have determined that the assassination would be an automatic success. Not only do the rules permit you to do that, but they encourage you to.
To be fair to the objecting player, this section of the DMG continues:
Only call for a roll if there is a meaningful consequence for failure.
When deciding whether to use a roll, ask yourself two questions:
Is a task so easy and so free of conflict and stress that there should be no chance of failure?
Is a task so inappropriate or impossible- such as hitting the moon with an arrow-that it can't work?
If the answer to both of these questions is no, some kind of roll is appropriate.
The objecting player might say that there is a meaningful chance of failure - but that is confusing a chance of failure with a consequence of failure. Setting aside the the 1-in-8000 chance1 that the rogue would 'miss' the first round, even if they hit and do many dice worth of damage2, it is possible that the NPC might survive after the first blow if the rogue rolls very poorly on all those dice. So yes, they might not kill the NPC after one hit, but what happens then? If there are guards near enough that they can be alerted with one cry, then your rogue hasn't really done all the preparation necessary for automatic success. But if what this really means is that you will play out two or three rounds of combat in which the rogue fights an unarmed and unarmored opponent who has only a few hp left, then there isn't actually a meaningful consequence of failure. It is just prolonging a forgone conclusion.
Is this combat?
One might be skeptical that an assassination attempt can be compared with walking across a floor. Can a DM actually permit a PC to kill an NPC without combat? Well, what is combat, according to the PHB?
The clatter of a sword striking against a shield. The terrible rending sound as monstrous claws tear through armor. A brilliant flash of light as a ball of flame blossoms from a wizard’s spell. The sharp tang of blood in the air, cutting through the stench of vile monsters. Roars of fury, shouts of triumph, cries of pain. Combat in D&D can be chaotic, deadly, and thrilling.
Does this sound anything like the assassination attempt? D&D is not a simulationist game - it does not attempt to realistically portray the damage a blade might do to the body of an opponent, nor the chance of being able to place it correctly. Rather, it attempts to capture the drama, struggle, sturm und drang of violent conflict. Presumably your rogue has had this experience already - securing floor plans of the NPC's lair without knowing whether they were accurate, sneaking in and overcoming the guards through stealth checks and perhaps even combat. What remains is not tension and excitement, but dramatic reward for their efforts. If there is any chance the NPC will live, that they will be able to call out and bring aid, that they will be able to reach their potion of gaseous form and escape, then you should roll out the combat as normal. But if you have extracted the last drop of drama from the situation, it is no longer a combat; it is just tedious dice rolling. If the NPC survives the first blow, but is severely wounded and cannot realistically harm the rogue before they are cut down, spending those few rounds of rolling does not create the excitement that combat is supposed to engender. Rather it removes the drama and replaces it with frustration.
In the game I DM, the party is currently in the underdark. They came upon, and had to pass through, a partially collapsed tunnel whose near end was infested by shriekers. The shriekers themselves posed no combat challenge to the high-level party, but the possibility that they might shriek and warn or attract other monsters did. The ranger approached carefully - was his Perception good enough to see them all? Was his Stealth good enough to get a spell off (silence) before they could note him? Was his Arcana good enough to place the spell to include them all in the area of effect? That was the drama of the situation. Once those had all been accomplished, the mage remained at a distance and roasted them all with firebolt. Now I could have forced the mage to roll to hit, because a miss was possible. And I could have insisted that she roll damage, because even with 3d10 a low roll might result in a shrieker surviving. But at this point, we were no longer in combat. Absent dramatic tension, it was just dice rolling. The only consequence to not one-shotting a shrieker was that the encounter would take six seconds longer of game time so that she could roll again. Once the ranger had achieved his goals, I just narrated the mage roasting the shriekers without a roll being made.
Consider what the DMG (p. 82) says about Combat Encounter Difficulty:
There are four categories of encounter difficulty.
Easy. An easy encounter doesn't tax the characters' resources or put them in serious peril. They might lose a few hit points, but victory is pretty much guaranteed.
What about situations even less challenging than easy? If your rogue, like my mage, faced a situation that did not use their resources at all, put them in any peril, and in which victory was guaranteed, that is not a combat encounter. Getting to that point was likely several combats, but once the rogue's knife was against their helpless opponent's throat, it is no longer combat. One might think that "Attacking a creature is pretty much a call for an attack roll by the book," but remember what the PHB says:
If there's ever any question whether something you're doing counts as an attack, the rule is simple: if you're making an attack roll, you're making an attack.
Here, the inverse applies - if the DM doesn't call for an attack roll, you aren't making an attack.
What are hp?
Hit points represent a combination of physical and mental durability, the will to live, and luck.
During the rough-and-tumble of combat, the NPC's trained combat reflexes make most blows that land wounds, and they survive those wounds through a combination of durability, will to live, and luck. But sleeping is simply a different story. It is perfectly appropriate for you to rule that no amount of will to live helps you when a trained assassin has slit your carotid artery with a sharp knife, and no amount of luck is of aid when they later plunge that knife through your eye and into your brain stem. In this case hp are not relevant; you simply die. If an NPC was on the executioner's block, I would not worry about how much damage an axe does; no amount of hp keeps you alive after decapitation. Despite the objecting player's min-maxing optimization of damage in combat, this is not a combat situation, and the the concept of hp don't apply.
As SeriousBri states so well, theirs is not a rules objection so much as an existential crisis in realizing that they are not prepared for all aspects of the game. I join NautArch's call for SeriousBri to submit their insights as an answer so that we can all upvote it.
1 With proficiency bonus and dexterity mod against an unarmored opponent, they are probably going to miss only on a natural 1. They have multiple sources of advantage (unseen attacker, unconscious opponent, possibly assassin subclass with a surprised opponent), so only a 1 in 400 chance of rolling 2 x 1N. In that unlikely event they can use a free object interaction to draw a second blade and attack with a bonus action a la two-weapon fighting for a third chance to hit, so only 1 in 8000 chance of rolling 3 x 1N.
2 So long as they hit with a source of advantage (unseen attacker, unconscious opponent, possibly assassin subclass with a surprised opponent) they can use their rogue Sneak Attack, and this dice pool will be doubled since all of the rolls are automatic criticals (attack on unconscious opponent, possibly assassin subclass with a surprised opponent).