A public field is not worse than a getter/setter pair that does nothing except returning the field and assigning to it. First, it's clear that (in most languages) there is no functional difference. Any difference must be in other factors, like maintainability or readability.
An oft-mentioned advantage of getter/setter pairs, isn't. There's this claim that you can change the implementation and your clients don't have to be recompiled. Supposedly, setters let you add functionality like validation later on and your clients don't even need to know about it. However, adding validation to a setter is a change to its preconditions, a violation of the previous contract, which was, quite simply, "you can put anything in here, and you can get that same thing later from the getter".
So, now that you broke the contract, changing every file in the codebase is something you should want to do, not avoid. If you avoid it you're making the assumption that all the code assumed the contract for those methods was different.
If that should not have been the contract, then the interface was allowing clients to put the object in invalid states. That's the exact opposite of encapsulation If that field could not really be set to anything from the start, why wasn't the validation there from the start?
This same argument applies to other supposed advantages of these pass-through getter/setter pairs: if you later decide to change the value being set, you're breaking the contract. If you override the default functionality in a derived class, in a way beyond a few harmless modifications (like logging or other non-observable behaviour), you're breaking the contract of the base class. That is a violation of the Liskov Substitutability Principle, which is seen as one of the tenets of OO.
If a class has these dumb getters and setters for every field, then it is a class that has no invariants whatsoever, no contract. Is that really object-oriented design? If all the class has is those getters and setters, it's just a dumb data holder, and dumb data holders should look like dumb data holders:
class Foo {
public:
int DaysLeft;
int ContestantNumber;
};
Adding pass-through getter/setter pairs to such a class adds no value. Other classes should provide meaningful operations, not just operations that fields already provide. That's how you can define and maintain useful invariants.
Client: "What can I do with an object of this class?"
Designer: "You can read and write several variables."
Client: "Oh... cool, I guess?"
There are reasons to use getters and setters, but if those reasons don't exist, making getter/setter pairs in the name of false encapsulation gods is not a good thing. Valid reasons to make getters or setters include the things often mentioned as the potential changes you can make later, like validation or different internal representations. Or maybe the value should be readable by clients but not writable (for example, reading the size of a dictionary), so a simple getter is a nice choice. But those reasons should be there when you make the choice, and not just as a potential thing you may want later. This is an instance of YAGNI (You Ain't Gonna Need It).