We go to great lengths to avoid outright breaking people's games. We carefully note any breaking changes we make in the release notes, and try to make as few of them as possible.
The immediate reason Local Storage exists is to support the Chrome Web Store. Google removed support for WebStorage in Chrome Web Store apps, so C2 users had no way to store data there unless we started using a newer and incompatible API. There are several other benefits though, including improved performance and higher storage capacity, outlined in the r202 release notes (where it was first released). There is another reason the change was made: the underlying API the WebStorage plugin uses is widely criticised by web developers for being limited and synchronous (i.e. it will freeze the entire page/game while it works, which makes things incredibly janky if the storage device is slow). Browser makers also don't like it for similar reasons, and is why I think it was removed from the CWS. It's basically seen as a mistake which needs to be replaced by something else and then removed. It is definitely better to move off it while it's still supported. This means nothing is immediately broken, and people have plenty of time to update or decide to stick with WebStorage for the time being. A few years in future it may eventually be removed, and the damage would be significantly reduced by the fact we moved to LocalStorage a few years in advance. On the other hand we could have left WebStorage there, and when it eventually got removed it forces everyone's hand: your game is currently broken, until you move to a new feature, and then there's a big panic and hurry and probably long complaints on the forum about how people's games randomly break. So while the transition to LocalStorage is a little tricky for some since it works slightly differently, I think it's definitely worth doing sooner rather than later. Deprecating WebStorage is a means of discouraging use of it, particularly for new users, and helping them avoid getting caught out by future removal.
tl;dr - we really try to avoid breaking changes, and when we do, it's usually for a good reason, and done to minimise the overall damage in the long term.