At the moment, there are many blocks that are missing a testing generator and trying to create them in a Behat test throws the following error:

Component block_XXXX does not support generators yet. Missing tests/generator/lib.php

However, if you try to implement the generator you will find that you only need to extend the testing_block_generator class without implementing any method or adding anything that couldn't be inferred automatically.

Keeping that in mind, we could provide a default generator for blocks that don't define their own. If any block still needs specific functionality, we can always implement a specific generator to replace the defaults.