Objects are all about making state explicit. Constructors connect different primitive values to a higher order concept, goal or task and checks invariants; The object's class gives the primitives a type which IS a form of state. A Year(2005) could guarante that the integer is > 1970; an int can do that on its own. 'hello@example.com' is not just a string; it should be an Email address and modelling this with an explicit class communicates state: that string is not just any string (all of Shakespeare's work in mandarin in base64) but a specific kind of string (an Email address). The mere existence of a valid object then communicates state, as do all types. I'd argue: Objects are all about making state explicit.
Still, it is really easy to abuse objects and make state implicit as you described above. I would argue that getters and setters are plain wrong to begin with, but that is a nother topic.
For example, if you do `Wallet.pay(amount)`, Ideally, you should get a new instance of a Wallet with the reduced amount, instead of reducing the internal credit variable. For many, this seems to be the wrong kind of modelling though, because when immitating the real world, you don't copy-clone your wallet physically when tipping a waiter.
Objects can and should be created immutable, but then, sometimes working with state is fine. For example an iterator (calling `bookmark = Boomark(book); bookmark.next()` a hundred times gives different page each time).
Imagine OpenGL; you send a lot of data to your graphics card and then tell it what to do with that data. Sending data is quite expensive. During rendering, you tell the pipeline what buffer to bind and what to draw at a single point in time (i.e. a frame). This is easlily represented by objects that keep track of the state. Your object-graph just remembers what buffers are bound. I, too have seen tangled and messed up designs; but I would still argue that thinking in state (my change does not go away) is intuitive for many people. Why not model systems that work like this explicitly? Shoehorning this into stateless pipelines can be quite difficult.
The problem isn't functions or objects (thats just fancy pointer syntax really) but that noone has figured out how to modell processes that work on symbols that change over time properly.
We won't fix this issue here; let's agree that we all like our state as explicit as possible as to avoid surprises and relieve or working memory.