Why use 'Getters' and 'Setters' to access private properties in PHP objects?

That's a good question. Getters and setters have advantages and disadvantages to consider, however to answer your question, I'll focus on advantages.

For example, when using a setter, the setter function could perform checks on the provided value, to determine if it's in range and/or a valid setting. If the value provided is erroneous, you could either continue using the last known good value (the one already set), or even go into a fail over condition or safe state, if such input is vital for proper or safe operation.

In the case of getters, you might want to trigger some type of action (such as logging) when a value is retrieved.

There are other considerations, of course, but this is what came to my mind at the moment. You might also want to look at magic methods, as a third option, just to give yourself an understanding of alternative options.

You might consider the following article, if you want more details on the advantages and disadvantages of each option, and which cases you might use one or another method.

http://russellscottwalker.blogspot.com/2013/09/public-properties-getters-and-setters.html

I hope this helps! Happy coding! :-)