Why shouldn't tests be run on a production server?
From semantic-mediawiki.org
Is it just because of performance concerns? Because then you can still run them when setting up the wiki.
It is an established practice that you run tests (unit or integration) not on a production cluster unless you have a specific task you'd like to verify.
Aside from the mentioned best practice, tests try not to leak any setup information (meaning any data required for the tests) into a test/production database by cloning all tables into a different namespace (prefix) but it may happen (happened in the past as we rely on MW's `CloneDatabase` but I haven't seen it happen as of late).
