By making it a state unit, the local police wanting a SWAT raid would not only need a warrant, but also have their warrant and reasons be convincing to the SWAT commander who is not under their chain of command, and who does NOT want to be associated with a major screwup in judgement.
By making SWAT consist of a few units in the state, it would be possible to have SWAT be better trained and equipped, and also faster to deploy, since it would become cost-justifiable to give them helicopter transport.
I wish the "real" SWAT teams--those that existed before every two-bit police department decided it needed to have one--would speak out against the proliferation of SWAT-wannabe teams. It is reasonably debatable whether there is a need for "real" SWAT teams; there is no justification, however, for many of the SWAT-wannabe teams. Not only do their tactics recklessly endanger innocent people, but they would also recklessly endanger the lives of the officers involved if their targets were anywhere near as dangerous as they claimed.