In MySQL 5.7.3, this behavior was changed. While the default is still as loud as it can, you can now add an option (log_error_verbosity) to send only errors to STDERR, which allows you to hide the output of mysql_install_db, and still get the errors, if they occur.
However, the same obnoxious verbosity is also in MariaDB 10.0.x. Since I discussed this specific bug with a few MariaDB developers early in 2012, I was disappointed to see this same output when running mysql_install_db with MariaDB. Here’s the same appeal: MariaDB developers, please fix this usability issue!
And now, for the laughing notes. All versions of MySQL available now, from Oracle, Percona, MariaDB, list this line when installing with mysql_install_db:
Please report any problems with the './scripts/mysqlbug' script!
There is Bug#29716 that was reported in 2008, about mysqlbug being unnecessary (by then, it had been obsolete for 2 or 3 years already), with a patch submitted but not committed. So, in 2013, we still see a reference to a tool that has ceased working for at least 8 years. It should not take much to remove this line and replace it with an appropriate link to the bugs system.