Well yes, that's a given. Charm person isn't mind-control. You still have to influence the person. That's exactly why the charmed condition gives you advantage on social interaction rolls on them.That's one way to run it.
But with the merchant, there is cost involved. AND there the "A successful charisma check MIGHT be required..." So an equally valid way to run it is if the outcome is not in doubt, no amount of friendly or charisma is going to make a difference.
But charm person makes the person friendly, and a friendly person is automatically going to help you in some way, according to that table in the DMG. The roll is to determine how far they are willing to go. And even assuming a Charisma of 10 and no proficiency in any Charisma skills, with advantage you will on average beat a DC 10. Which means minor risk or sacrifice.
Which means if a completely average caster charms a typical NPC merchant, they can likely get at least a minor item for free or at serious discount. Whether the item the PC wants is considered minor depends on a lot of things, of course.
That's why I kept talking about the personality of the merchant. Scrooge--pre or post ghosts--is not a typical NPC merchant. He has a name and probably a fully fleshed out statblock and TBIF section.That means that even if your wizard comes up to Ebenezer Scrooge(pre-ghosts) and casts Charm Person on him, Scrooge isn't going to give him free money, friendly or not. He would still want you to succeed in getting the money you are asking for, and would very helpfully give you directions to a different money lender, but would not give it to you himself. The outcome is not in doubt. You wouldn't be getting free money from Scrooge, no matter what your persuasion ability.
But OTOH, imagine if the PC is, say, a 10th-level bard with 20 Charisma and expertise in Persuasion? That's +13 to the roll, with advantage and who knows what other sort of bonuses (maybe the cleric cast guidance on the bard; maybe the warlock cast bane on Scrooge), who then gets to roll with advantage? Yeah, I might allow it. When you get people who can roll a 30 or higher on their Persuasion checks, you can allow these sort of shenanigans.
Especially because 10th-level bards are not 14th-level enchanters, and thus both Scrooge and the typical NPC merchants will know they were charmed. And they likely have the ability to make the PCs' lives less happy because of it.
Also, don't forget that Scrooge was stingy because he didn't want to spend money on amenities for himself or for decent wages for his employees. But if the PCs are posing as investors of some sort, who will use Scrooge's money to make him a ginormous profit? That'll likely bypass the stinginess and amp up his greed.