The trouble with providing systems for things like "Make the noblewoman Elisha like you more" is that the system ends up being utterly silly and breaking immersion. A single conversation doesn't take a week and if Elisha is actually important to the story then presumably the conversation with her is interesting enough to roleplay out, not roll out. If Elisha isn't important then are the players really even going to know who she is? Are they going to care about trying to make her like them more? Is a numerical system to handle this going to be any use since you aren't going to show them the results anyway? If they do upgrade her attitude from Neutral to Friendly they shouldn't actually know that for sure.
A weekly system of chores does actually make sense when governing things like crafting objects, doing a job for cash, or building a tower. Unfortunately although it makes sense it still isn't any use. If you do want to build a system that allows characters to do labour for money you also need to keep track of their trivial expenses. Does anyone really want to spend the time to figure out how many copper pieces they spend on bread and their profit margins on a being a part time carpenter? In a traditional game characters are so rich those sorts of things become irrelevant chump change by level two and in a non traditional game people aren't tracking their income from tradeskills. You certainly can build a reasonable system to govern these sorts of tasks but I can't fathom why you would want to bother.
There are all kinds of weird economic systems in previous versions of DnD and the main thing about them is they were totally irrelevant until somebody abused them horribly. People would try to hire thousands of soldiers to defeat dragons for them, abuse crafting laws to generate astronomical sums of money, or start magical item factories. I have never seen those sorts of systems actually provide anything of use since it was so easy to simply roleplay through them instead. Trying to do a combat in a heroic fighting game doesn't work without the numbers but that shouldn't confuse us into thinking that we need numbers for everything or that we need absurd structure for social interactions.