It will need some time to port all these projects over to 1.1 but everyone can easily see the benefits. Supporting both will be a nightmare. Just drop 1.0 support and require 1.1
The point is applications won't be able to easily do this. As the post points out it's likely many distributions will adopt the 1.0 release series due to the length of support. So if you only use to 1.1 API you may find the burden of installing another OpenSSL release is placed on your users as their base system contains a version of OpenSSL with an incompatible API.
To be clear I think the API change has good intention but it would be been nicer to have marked parts depreciated and introduced new interfaces more gradually. OpenSSH is a good example of this in terms of advertising ahead of time breaking changes.
-The API changes are needed and good
-The migration to 1.1 will be difficult