Why, though? If it matters to the game world then it matters to the game. If I spend my years between adventures becoming a reknowned artist, that matters to the game as much as it matters to the story and the world it takes place in. Imagine the connections I would have forged between nobility, how did I use my art to influence culture? Did I extract huge sums of money for my work? Do I return to the party vast sums of wealth?
Which at its core reads to me like "I'm not going to actually play through whatever you want to do, so just make sure whatever you do has no fundamental impact on anything." Heck, lets run with your example: there's a gang of were-rats, that is: a gang of humanoids with a highly infectious curse running around town. "Cleaning them up" has meaningful impact. Not just that you cleaned them up, but how you cleaned them up. Did you kill them? Was one of them perhaps a long-lost son of someone important? Did you save them and same question?
If the were-rats are worth no XP, and have no fundamental value to the story other than being a minor irritation to the town, why where they there? Because to me it sounds like this thing that wasn't any trouble, and wasn't really causing that much harm, really didn't need to exist in the first place. It sounds to me like your veto power comes into play right when these things would start to matter.
And also: I only got it from your post, not anyone elses.
Lol no. Because I don't run downtime like that. Downtime isn't a little homework exercise everyone just invents for what happened between now and the next problem. I actually run downtime. It's a thing we all do, together, at the table. Maybe we don't all take part in each other's individual activities, but we are all at the table, taking turns, rolling dice, seeing how the outcomes of our "downtime" turn out.
It's not story time. Ya'll can go home and make up whatever stories you want for your characters. Kill Asmodeus if you want, I don't care. But if it didn't happen at the table, it didn't happen in the game, and it sure as heck doesn't affect the world.
The PCs don't cease to exist simply because there is no game session and because I don't feel the need to play a mini-game surrounding down time. In my campaigns PCs can do things that affect the wider world during their downtime if it makes sense for the story. By taking out the wererats, the syndicate potentially lost an ally and the streets of gutter town are safer for the time being. The PC gained some enemies and some allies which very well might play in to the larger story.
As far as the outcome of the confrontation with the wererats, this is something we work out between the player and the DM between sessions. The player suggests a general outline, DM approves or tweaks, player does draft(s) that get reviewed, etc. When it's all done we post something so everyone can read it. If the entire scenario is too critical or important, it doesn't happen off-screen. Or perhaps the next session picks up with the rest of the group rescuing the PC in question because they got in over their heads.
In another scenario a PC wanted to have their wedding done off screen. I wanted it to happen during a session because I thought it would be fun RP for the group and there were some interesting reveals/decision making to do. There were no alternate dimension Nazis interrupting the wedding, no fights, but there were aspects that mattered to the entire group so it didn't happen off-screen.
Ultimately I view XP, GP, magic items as rewards for playing. D&D is not a reality simulator and as much as I try to make the world logical and consistent, I also don't feel the need to reward people's PCs with rewards for things that happen between sessions.
You know my entire post wasn't responding to you right?
You know that people can respond to posts not directed directly at them, right?