Well, I've tried clearing them in VS (Player VS Player) before, and never had one work. But I don't play the game as often. If player vs CPU works and Player Vs Player doesn't... ugh. I tried clearing the Shibusaki Request this week in 2P VS and training, and it didn't clear until going to Sim's story and fighting a particular battle. If other ones work (or even that one), good, at least it's something, and the biggest pay-out something. I've tried breaking the signs and such in multiple VS matches, never got a thing. Then went into 1 online or training match, and had them pop after.
Injustice stuff all has a real money value attached to it's DLC stuff. You can earn their premium coins and use them to buy the costumes and such. Maybe not the characters themselves, but they also don't break down every little color and stage into separate money purchases. Local VS doesn't directly earn chest, but leveling and stuff still happens, so it's got most of the perks of playing an online match. And for both players, for each of their accounts.
I wanna say I THINK you can use KI gold to buy a character (I always just got the full seasons), but if not, they have given away seasons on GWG, they have a free weekly rotating character, and they actively put sales on stuff. Even if you didn't buy anything more than S1, or get it for free, there's still big gameplay reasons to come back weekly to try out something new. Not entirely comparable, sure, but at least more inviting and aware. They don't let 2P earn anything, but they let P1 level up with offline VS play.
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Capcom had 2 separate credit systems to start off. It still feels incredibly off to me that not only do I not earn anything on my account of offline VS play (Save for the possible one weekly achievement you mention), but the other person has no personal account access, and earns nothing either, even If they play on another actual profile. If they wanted to lock off earning characters through VS play because it could be exploited, they still could have given access to earning stage variations, colors for costumes already unlocked, or titles, frames, exp for lvling up, offline lvls that lead to unlocks like T7... anything.
Just sucks that the majority of time I'll spend with the game, doing the same stuff, is a virtual black hole of almost no worth, especially because there's so much usually free junk that has been split for the sake of sapping Fight Money. Would be nice if they had a Tournament Mode built into the game, like DOA 5. Then at least I wouldn't have to put in double work to earn stuff for characters I don't play too, so that local VS opponents could use them off my profile.