With config.yaml including simple-form logging config:

logging:
  distributed: debug

>>> import logging
>>> import distributed
>>> logging.getLogger("distributed")
<Logger distributed (DEBUG)>
>>> logging.getLogger("distributed").handlers
[<StreamHandler <stderr> (NOTSET)>]
>>> logging.getLogger("distributed").debug("debug")
distributed - DEBUG - debug
>>> 

All looks good. Start a Client:

>>> from distributed import Client
>>> c = Client()
>>> logging.getLogger("distributed")
<Logger distributed (DEBUG)>
>>> logging.getLogger("distributed").handlers
[<StreamHandler <stderr> (WARNING)>]
>>> logging.getLogger("distributed").debug("debug")
>>> 

No logging output, as the distributed logger has had its Handler (a StreamHandler) set to WARNING threshold.

Once a Client is started and fires-up a local cluster/scheduler, I suspect a worker:

... runs silence_logging, which does just as it is named:

See also #2659 . It might be argued that nothing important is logging to the distributed logger, and everything is logging to a child e.g. distributed.client (even through the loggers are flattened with the simple config), which might be true, but it further erodes the notion of hierarchical logging.