I really recommend you read over the FAQ that is in the proposal at [0], it answers most of your questions.
The problem is that it seems a "private by convention" system isn't private enough for many library authors, who are finding their private internal methods being used regardless, and then after some time becoming ossified leaving the maintainers in a tough situation. Support the "private" interface even though they shouldn't have to to avoid breaking a significant number of users, or break the "private" interface and leave many developers with code churn.
Regardless of where fault lies (often times it's one library using the private interface of another library, and the developer gets caught in the middle), this is a bad thing, so people began workarounds like complicated closure systems or weird-looking interfaces which emulated true private fields without having support for them.
This started becoming popular enough that it was decided that adding them to the official syntax would be better, and unlike in PHP or other languages, there is no way around it here. Serializing or casting the object doesn't expose private fields, and there is no reflection methods or anything that would allow it. They are truly private.
I personally share your feelings that this isn't an issue that needs solving (i'm of the opinion that the lack of easy truly private properties had a non-zero impact on the rise of javascript, and the ability to tweak private interfaces in your code is a net benefit, even if it gives developers rope to hang themselves with), but the pain felt from it is real for many, and the workarounds they were using were not only slow and difficult to use and maintain, but also very hard to understand, and this alternative is a much better solution in my opinion.
So while I most likely won't be using them, I reluctantly support them being added to the language.
[0] https://github.com/tc39/proposal-class-fields/blob/master/PR...