Completely re-factored the Sidebar Block system as a precursor to this. The idea was that if you are creating custom HTML blocks, you might want to have more than 1 at a time. The database and caching have been updated to reflect this and to allow the future-feature of configuring blocks on a per-area or per-page basis.
Sidebar Blocks are now created based on primitive block-types. In theory you can now have 7 sidebar searches on the page, although I don't know why you would want to
So in the next release, you will now see controls to delete sidebar blocks as well as create new ones.
There is now a section for managing the installed block-types if Debug Mode is turned on. This should help modders figure out what to do (it explains what classes you need, etc) and at least take care of creating the database record for them.
Readability Score and Similar Content are now not created by default, but the types are there, should you want to add them as blocks. This doesn't affect users who already have those blocks created from earlier versions, but they can certainly delete them if desired.
And finally, the feature requested in the OP is available in the next release. Simply create a new block from the 'Custom HTML' type.
Still need to create all the phrases and I think the workflow for creating blocks from types can be simplified, so I'm leaving this as In Progress.