Social skills: role-playing versus roll-playing

You know how the argument goes:

Person #1: "I am old-school! I do not allow my players to roll diplomacy*! If they want to convince an NPC, let them role-play it!"
Person #2: "But the diplomacy skill allows a shy player to play a persuasive PC!"
Person #1: "This is a role-playing game! If the player does not know how to role-play, he will learn during the game!"
Person #2: "Oh, great, do you make your players swing swords to lean about fighting too?"
Person #1: "No, since we obviously cannot do real combat! But I don't let them roll to find traps! They just describe what they are doing!"
Person #2: "So do you solve combat by describing sword blows? And why do you have a Charisma stat in the first place?"

...etc.

* Or "roll Charisma", "make a reaction roll", etc.

I have little interest in this discussion because I am convinced that the truth lies in the middle. In fact, I am half-convinced that MOST OF US agree the truth lies in the middle. The problem is that we are discussing IN THE ABSTRACT. But discussing how it goes IN PRACTICE is easier and more useful. Let's try.

Scenario: PC wants to buy a new sword. The (female) blacksmith says it costs 100 gp. PC has 70 gp only.

Example 1:
PC: "100 gp? I only have 70 gp. Could she give me a discount?"
GM: "Nope. She says she will go out of business if she does"
PC: "Can I roll diplomacy?"
GM: "No need, she already refused your offer".
PC: "Can I try to convince her?"
GM: "Okay, what are you going to say?"
PC: "Madam, I will pay you when we come back from the dungeon! With 10% interest!"
GM: (after thinking for a second): "Nope, she just met you".

Example 2:
PC: "100 gp? I only have 70 gp. Could she give me a discount?"
GM: "Nope. She says she will go out of business if she does"
PC: "What? We just saved the village!"
GM "Yeah, you're right. I remember what you did, brave adventures. We will forever be grateful! I will give the sword for your gold! I have mouths to feed, but it is the least I can do!"

Example 3:
PC 1: "100 gp? I only have 70 gp."
PC 2: "Wait, I have 15 gp here"
PC 1: "Could she give me 15 gp discount?"
GM: "What are you saying to her?"
PC 1: "Madam, I do not have the gold you need at this moment, but I will come back with the difference after we defeat the goblin horde!"
GM: "Okay, roll diplomacy".

Example 4:
PC 1: "100 gp? I only have 70 gp."
PC 2: "Wait, I have 26 gp here"
PC 1: "Could she give me a 4 gp discount?"
GM: "Sure."
PC 1: " Do you want me to roll diplomacy?"
GM: "No need... it is not like she has lots of business anyway".

Example 5:
PC: "100 gp? I only have 30 gp! Could she give me a discount?"
GM: "Nope. She says she will go out of business if she does"
PC: "What? We just saved the village!"
GM: "Yeah, you're right. I remember what you did, brave adventures. I really want to help, but I cannot sell you the sword at this price! I have mouths to feed!"
PC: "Madam, we will come back after we defeat the goblin horde and pay you in full!"

GM: "But what if you perish? My children will starve!"

PC: "I swear by all the gods we hold dear, I will fulfill my duty, and even if I fall my companions will not let my debts go unpaid!"

GM: Okay, roll diplomacy.

Example 6:
PC: "100 gp? I only have 50 gp! Could she give me a discount?"
GM: "30 gp? Nope. She says she will go out of business if she does"
PC: "What? We just saved the village!"
GM: "Yeah, you're right. I remember what you did, brave adventures. I want to help, but I cannot sell you the sword at this price! I have mouths to feed!"
PC: "Madam, we will come back after we defeat the goblin horde and pay you in full!"

GM: "But what if you perish? My children will starve!"

PC: Is she wearing that Bahamut pendant some smiths use?

GM: (after thinking for a second): Yes.

PC: "I see you are one of the faithful... Madam, I fight for the honor and glory of Bahamut, and he will never let me perish before I fulfill an oath! GM, I uncover my shield and show her the symbol of Bahamut!

GM: I believe you sir! Take the sword! May it bring glory to Him!

And so on.

In short: when most possibilites of role-playing have been exhausted, and the result of the interaction isn't obvious, then you roll the dice.

I think the same idea can be used to find and disarm traps, solve riddles, and even in combat in some circumstances (PC: "I cut the prisoner's throat! My attack bonus is..."; GM "No need to roll, the prisoner dies").

In short, there is nothing really unique to "social skills" in this regard. You describe what you want to do and, if the outcome is uncertain, you roll. Had a clever idea? Maybe the outcome is now certain. Maybe you roll with advantage. Etc.

BTW, the original edition of D&D let Charisma define loyalty of your hirelings and "whether or not a witch capturing a player will turn him into swine or keep him enchanted as a lover", so there was definitely an aspect of character "skill" to interactions - which is why I don't think ignoring social abilities is particularly "old school".

In conclusion, while I may enjoy discussing "role-playing versus roll-playing" and other abstract issues, sometimes I feel it is a waste of time - unless we can use these discussions to make our games more enjoyable, which requires using these ideas in practice.