I too have been caught out by this feature. It seems unintuitive for the interface to allow you to reassign the configuration to a new user but for that (deliberate) act to not actually do anything. The test manager sees the configuration assigned to a user but the user does not!
I have found a work-around is to re-assign the configuration, disable the configuration and save the test plan. Then enable the configuration and save the test plan again. This provides the desired action of re-assigning a configuration to a different user.
Performing a mass assignment adds a comment to the test run which may be advantageous for version tracking but adds a comment to each test run which may be undesirable.
May I suggest as a temporary solution for uninformed users (like me) that reassignment of a configuration is accompanied with a popup dialog which warns the user that the test runs will not actually be reassigned but also informing the user that disabling the configuration, saving the plan and then enabling the configuration will re-assign the runs? (I don’t know whether that is simpler than offering the option to re-assign the existing runs which might be better / preferred behaviour.)