What is the purpose of this lockout on a dishwasher / disposal circuit?

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As required for hardwired appliances so they can be serviced.

While not being serviced the breaker is locked “on”. Does the breaker have an internal trip so it will trip when it needs to?

It isn’t locked on. The device is so that it will be locked off. A breaker will trip even if it was “locked on”.

Those applainces require disconnecting means as Stephen mentioned, which is typically a cord and plug. If they’re hardwired then a breaker lockut device can be used in lieu of the cord and plug.