I don't see why not.
You state that the characters have backgrounds chosen in regard to the other characters, the setting, and themselves.
- Ms. Dude, paladin*, affiliated with the Bright Temple, volunteers time performing charity works rather than training.
- Maisry, fighter, curious about the non-standard faiths, seeking to prove herself in battle, fearful of being or appearing weak.
- Anoixan, magician, deeply curious about magic theory to the point of seeking to learn different branches of magic, desires to make spells or items named after him.
- Lothric, cleric, devoted to the Lord Nergal, Patron of Defiance, Tenacity, Undeath, seeks deep communion with his Patron as he feels alienated from other people.
You state that they develop and resolve rivalries, gain friends, and accrue obligations.
Ms. Dude: Helps organize an orphanage paid via her share of the treasure. In order to obtain permission, grants, and rights for land Ms. Dude interacts with local nobles and arrivesti**. [Skills: Influence (Cha), Perception (Int), Gambling (Dex)] Through a grand success (very high roll) she meets and befriends Lady Doe, a third daughter of a noble family sent to the Bright Temple. A skilled healer, she accompanies her on adventures.
Maisry: Looking to outright murder the magician Stone, who has been a pain in the party's collective neck since they accidentally brought him back from the dead. She discovers the he is hiding out in Lady Pettigrew's mansion, and perhaps even her lover. She and a couple friends invite themselves over to the arrivest's mansion for the Lady's noted hospitality. They discuss, first obliquely, then directly, her relationship to Stone and where he might be. [Skills: Influence (Cha), Perception (Int); Contact: Noble] A marginal roll on Perception, modified by the use of a Noble contact to have the meeting, told me that the Lady Pettigrew had a minor son of the family Manderly was one of her bodyguards. If he was slain, and he was, Lord Manderly would want revenge.
Anoixan: Well, sometimes magic doesn't work the way you want. And, sometimes you have friends who want to do bad things and you have to continually hold them back. For someone who wants to gain fame through magical inventiveness, reminding your wizard buddy from a different guild that you can't experiment on the peasants gets to be stressful. After difficult magical experimentation using a very limited mind-expanding substance, he really didn't need to hear the horrible plan his dark wizard friend and Maisry cooked up. When he's not adventuring or experimenting, you can often find him drowning his sorrows at his favorite meadery. [Forget the skill checks, Magical Theory (Int) definitely, but he ended up with success, but you have to deal with the psychic pain somehow. Alcohol works for the character, however maladaptive. This was highly player driven, and not a twist I expected!]
Lothric: The cleric mentioned above, shadow girlfriend, the spells
hold shadow (Anoixan),
speak with dead,
lesser restoration (flex), Skills: Influence (Cha), Religious Lore (Int), Insight (Wis). He got a grand success on the Insight.
So,
Your players have characters with backstories.
My players have characters with backstories.
You have a mechanism that indicates a twist or complication should be introduced.
I have a mechanism that indicates a twist or complication should be introduced.
You have a method where players can negotiate narration of responses.
I have a method where players can negotiate narration of responses.
I grant that you have a system that is more elegant for that purpose. But do not assume that it is an experience foreign or rare to me.
* Paladins are not tied to a temple, and don't source divine power. They have an inner strength and true moral compass that allows them achievements beyond the typical.
** Arrivesti are, basically, merchants who purchased noble title.