It's certainly not the approach everyone would be happy with, but it allows developers much more flexibility than the contrary case, where private browsing is a silent effect that might make apps do very stupid things (like, say, downloading the same huge asset bundle into localStorage over and over.)
This would happen anyway no matter what storage or cache is used since all data is cleared after private browsing session is over.
Breaking localstorage (with an over-quota error) is not the way to deal with this. Polyfills are just more crap in complexity and downloaded bytes to compensate for a browser's issues.
It would be much better to have a navigator.isPrivate flag enabled so apps can check the environment accurately, not guess based on whether certain APIs work or not. It's not about SLAs but supporting standards. Deleting client-side data is all that private browsing needs to do.