Usually the problem isn't that the changes are big, but that the new way simply isn't compatible with the old way to do things, and you can't just make a change that will break existing applications in minor versions (well, there's nothing technically stopping you, and unintentional compatibility breaking bugs have definitely happened in the past, but people are gonna get real mad at you if you do that). Even if you break that change up into thousand tiny changes over many minor versions, the end result is that at some point, you break old apps.

The solution is to take note of all the things that are either badly designed or became obsolete and once in a while go "hey, let's make a new major version and fix all of this crap". With a new major version, you don't have to worry about old applications and are free to improve your library in any way you wish, and you also get the option to keep updating the old major version with some maintenance bugfixes so that the old apps keep working well enough.