It depends on the editor. It works fine with Redactor and TinyMCE, but like you discovered CKEditor and TinyMCE RTE need a bit more convincing. ContentBlocks does not contain Redactor-specific code (interestingly it does contain TinyMCE specific code as otherwise it would break on drag & drop), so that’s not the result of us trying to lock you in to Redactor or anything. That same problem also happens in other extras that support RTEs, like faqMan.
I don’t currently have a solution for it, we do have an internal issue to track it and, if we can find the time, suggest a fix to the relevant authors. I’d suggest reaching out to the developers for a solution.