This is a wide-ranging topic, but if I could distill it down to a single thought, it would be:
If your game's Challenge doesn't come from its real-time elements, don't award Income based on real-time elements, either. This runs a great risk of breaking your game's balance, and even worse, of encouraging your players to Idle (do something else while leaving your game on, so they have a load of money when they come back).
Games like
The Wall Street Kid,
The Swindle, or
Recettear, which have a fixed number of in-game days you have to complete your goal, could get away with this kind of Passive Income mechanic, because the lifetime amount of passive income you'll receive is not infinite, and you may need to spend (limited) resources or tie your money up for a tangible portion of the in-game days in order to increase your passive income. As
@JosephSeraph mentioned, Passive Income mechanics can also work in competitive round-based games like the Interest mechanic in
AutoChess, because every round you don't spend your money is a round where you're weaker than you would be (in comparison to your opponents) and risk putting yourself closer to elimination - essentially, it's a risk/reward mechanic and you can't gain the interest forever.
League of Legends and many other MOBAs, not to mention lots of board games, award passive income over time to the players (1 gold each second, etc.), but these Competitive games force players to keep making moves against each other, meaning that they don't discourage action/engagement, and the fact that your opponents are also receiving passive income means that the mechanic doesn't change the game's difficulty.
In a narrative-based RPG (or a Platformer or a Puzzle Game or really anything else that doesn't have some kind of Time/Turn Limit or an Elimination mechanic), you are very likely to hurt your game when you add Passive Income to it. These games are all about engaging with the game world at your own pace, and it's far more fun to actually engage with the game world (defeat monsters, find treasure chests, craft items) than it is to passively receive money. In a game with Passive Income, players who are struggling will often Idle (or do whatever is necessary to get the passive income, like run around in circles) until they have enough money to buy the power they need - and that's massively unsatisfying.
Final Fantasy 8 is one of the most infamous games for screwing up its balance and gameplay with its Passive Income system ("SEED Rank"), but the history of gaming is littered with examples of games that massively screwed their own design with some kind of Passive Income mechanic, and I can't think of a single example (outside of time/turn limits or competitive games) where it worked well.
I think
Star Ocean 3 only got away with it because Money and Items in SO3 (aside from the basic, super-cheap Blueberries/Blackberries) were more of a luxury than a core game mechanic, and because it felt so damn cool to patent an item and feel like you were profiting from it. These both helped reduce some of the "unfun" from the design, but there were probably much better ways those rewards from inventing new items could have been implemented than passively gaining money (royalties) over time. Perhaps you could have evangelized the spread of your items to different planets throughout the universe, and each time a planet started selling one of your items, you'd receive a large one-time royalty payment.