Link to a subject I found on the community here: https://communities.bmc.com/communities/thread/69994?tstart=0, I suggest this idea that was quite difficult to explain to our customers each time and that can be I think improved to simplify assignment on some modules.
In Change Management, for Change Managers and Coordinators, the group displayed are based on the Available Functional Roles within the group. Thus, for instance, for Change Manager, only support group with at least one people having Change Manager Functional Roles are displayed.
But for Incident Management, for Assignee Group, all the support group appears even if no one inside this support group have Incident Permission.
If it was very clear for us why in a technical point of view why we haven't the same behavior, it's more difficult in a functional point of view to explain: it should be better to only see support group for which people have right to work on the process.
To complete this topic, often, we have to made some customization to answer this need either by changing the "OOTB" menu either by using the Support Organization to define the module the group is used for.