So, you want to replace a system that gets you better prices with merchants with a different system that gets you better prices with merchants...
I want to replace a volatile system based on leveraging a blatant meta-game exploit with a more stable and coherent one, that scales reasonably. Yes.
The same "exploit" exists. Getting better prices with merchants is, at the end of the day, getting better prices with merchants. It doesn't matter if it's party reputation, or gifts, or choosing a specific character to do the trading. All are "meta" ways to get better prices. The only thing that I see that changes is that you don't have to give up any items/gold as gifts, thus adding more stuff to the pool of stuff you can sell, thus adding to inflation. It doesn't solve anything, it just moves the goal posts to something else. What makes me believe this? I have two save files running right now in Fallout 4 where my characters are extremely rich. I'm not able to bribe them with gifts, or to use charm to influence their prices, and they're capped at how much money they have to purchase what I may be trying to sell, and yet, I can still amass tons of money in game, even if I ignore perk magazines that increase my selling price and decrease my prices when I try to purchase from them.
The point being that, even if this system was removed entirely, currency inflation is going to happen. It's going to happen with what's currently in game, and it's going to happen with everything you've suggested, so nothing will change, regardless, and players that are wise to how these systems work are still going to be able to "exploit" them. So how is changing it from bartering for better prices to using the character with the best charisma to get better prices going to improve anything? What makes you think that players that are willing to "exploit" one meta system won't "exploit" a different meta system?