This is called ‘arguing for advantage’, and it’s not really a problem unique to DnD.
‘I should get X because of Y reason’ isn’t usually about the Y reason – the person just wants X. The Y can be anything, and frankly doesn’t matter. When your human perception and judgement (aka basic social interaction skills) tell you that someone is arguing for an advantage rather than for some other reason (because they think Y is more logical, because they think Y is a better story, because they don’t like Z for personal reasons, etc) you should simply say ‘no’.
You may need to say no quite a few times. The arguing for advantage may morph into other means of social pressuring, like vague blame, repetitive asking, calling-in allies, convincing the crowd, so on. It’s entirely possible for this to suck the fun out of the game and make continuing with that player entirely unworkable. However you have a considerable advantage in this situation due to explicitly being the authority, limiting the social pressure it is acceptable to bring against you and giving them an ‘uphill battle’ in attempting to gain the advantage they are seeking.
If need be, explain that in this game the DM is the final arbiter of all rules interactions and world setting. They should be impartial, like a referee, and consult the table’s preferences to make a good game but when it comes down to it the DM is the one who decides what rules are used, makes up new rules if necessary, arbitrates any disputes, and gets to say what hair colour exactly that npc’s beard is. That’s the basic rule of the game and it is what people agree to implicitly when they sit down to game with people.
You can also do the following things.
Provide examples of what advantages can be successfully argued for.
Or ‘asked’ for. The paladin asks if there is a church in the village? You answer ‘yes’. The fighter wants to know if after seeing an awesome polearm fighter he can go learn from him? Yes. You change the fighter’s Fighting Style to Great Weapon Mastery as well, as he’s now using a halberd rather than the two shortswords he was previously, to reflect the results of his character training with the Yuan-ti Spearmaster for those 3 weeks. The mage wants to use a readied frost spell to turn the falling poison rain into ice, so it bounces off the party’s raised shields rather than dowsing and poisoning them? Yes. By agreeing to more reasonable requests, you show the arguing player that things can be gained by toning down his demands – this often leads to the demands being toned down.
Talk to them out of game.
Explain that DnD is a cooperative game and you don’t want one character to be more mechanically powerful than the others as it makes your job harder. Likewise, that giving one player exceptions to the rules and not others both makes your job harder (have to remember two sets of rules) but is also unfair. Explain that GMing is quite difficult for both mechanical and storytelling reasons, and you’d appreciate their help in keeping it simpler. Accusations and further arguing are rarely helpful – informing them of your point of view in a non-accusatory way and thus creating empathy is likely to be more helpful.
Move the game along.
If a player is arguing with you about getting whatever, you can simply move the game along – turn to another player, and tell them that they ‘find the innkeeper’ or whatever they were doing before the arguing player redirected the conversation onto why they should have X. If the player is ‘interrupting’ to make his arguments, it’s rude – this will lead to less arguing overall, as you can also make the ‘sorry but said he wanted to do X, so i’m talking to him now after talking to you about how you want a Flametongue’ which is reasonable/sounds reasonable.
Ultimately this is a social problem. It is about someone not sticking to the implicit rules of an activity. It needs to be solved through that lens, and the RPG-specific tactics available are limited.
There’s also something else that you’ve hinted at.
You’ve talked about whose ‘fault’ the TPK was, used the term ‘power play’ without qualifier or explanation, and talked about how someone making a choice in-game is a ‘problem player’ behaviour (hiring or firing an NPC guide).
These are all red flags. A GM blaming a TPK on a player or players instead of acknowledging that as the designer of the world they have significant control over whether the party lives or dies, someone who does not qualify what ‘power play’ entails to them but assumes it is universal, and a GM who assumes that in-game actions are universally for out-of-game reasons, are all common red flags for negative GM behaviours and attitudes in TTRPGs. I have and will again avoid a game with a GM who talks about such things, expecting that at the table their game will just not be.. good.
While from your question I lack any detail at all to determine whether these hinted-at problems actually exist, i’d suggest in general that whenever you are trying to determine how to interact with someone in a positive way that you also look at your own behaviour in an objective and logical fashion to find out if your own preconceptions, expectations, or negative beliefs are exacerbating any problems with the situation.