Most standard Monolog (https://github.com/Seldaek/monolog/tree/master/src/Monolog) handlers handle their triggering internally, for example:
// https://github.com/Seldaek/monolog/blob/master/src/Monolog/Handler/PHPConsoleHandler.php#L76
public function __construct(array $options = [], Connector $connector = null, $level = Logger::DEBUG, $bubble = true)
Handler is registered like
$logger->pushHandler(new PHPConsoleHandler(/* ... arguments */));
Why not declare trigger level when registering the handler, like
$logger->pushHandler(new PHPConsoleHandler(), [Logger::DEBUG]);