Hello and thank you for your contribution!
However, maybe we should not completely remove that logging. Instead, why not log everything to the logging module instead, at DEBUG level? That way, you can still see incoming requests for debugging purposes

@dev-dsp Are you planning to fix this or should I close it?

I'd say we should just take the original code, remove the timestamp (as it's included in logging anyways) and log it to logging

    def log_message(self, format, *args):
        sys.stderr.write("%s - - [%s] %s\n" %
                         (self.address_string(),
                          self.log_date_time_string(),
                          format%args))

to

    def log_message(self, format, *args):
        self.logger.debug("%s - - %s" %
                          (self.address_string(),
                           format % args))

closing, I'll implement the solution mentioned and open a new PR.