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Well, look at the Sydney Lindt cafe siege. Tactical Assault Group East (TAG-E), were not brought in because it was a single perpetrator, it was a window-filled open cafe and Police capabilities were considered to be more than enough to end the siege violently or non-violently. Capabilities matter more so than the extent of your mission profiles. An active CTU is always at the ready. There is nothing on their plate but CT and AT. If something is not given to them, they can still act as domestic advisors for the event.
Have a read:
There are similar pieces of writing out there, especially in regards to the legality and deployment of CTUs.