Persuasion rolls and diplomacy checks or anything of that kind are for selling NPCs on terrible proposals or lies. If a player makes reasonable arguments that would be in an NPCs best interest to follow up on, then I will use my role as GM to make that NPC agree with the player. No kind of roll is necessary.
It's only when an NPC does not want to do what the players want, or their arguments seem highly doubtful, that players may make a roll on the relevant ability to maybe be able to convince the NPC otherwise.
That is how I do it, too.
I have NPCs react to PCs in the way that I think they would, given the personality of the NPC, the situation, and what the PC says. I reserve rolls for cases where the NPC would not react in the way the player wants them to, but the player really wants to try to push things. Anyone can try to reason with an NPC, barter, or even tell a convincing lie. Rolls come in when those things don't work on the NPC, and the player specifically wants to try to be more persuasive.