If you're interested in games that aren't MMORPGs, Path of Exile fits your criteria for monetization. You can only purchase cosmetics and bank storage upgrades. It's an online ARPG but it's mostly single player.
It is pretty much unplayable without the bank storage upgrades though. Given the amount of time they can save you, you may as well say that they are power.
Right but there is no whale bait that impacts your sense of progression. All you really need is a one time purchase. Maybe $30 max to get all you need to out of storage and trading?