Michael is risking allowing Anson to reformulate his evil organization by giving him access to time and resources, all to save IRA terrorist Fiona. The risks, thus, go way beyond Fiona. Sure, if Michael kills Anson, Fiona goes to jail.
But ... but ... in the course of trying to figure out a way to save Fiona, he is risking a lot of other people. Already, numerous people have died while Michael figures out his plan. Every person who dies at Anson's hands adds to the cost of saving Fiona. From a strictly utilitarian viewpoint, the battle is already lost. Innocent people are already dead just by allowing Anson to walk around.
On the other hand, it adds a nice dramatic tension.
Yes, I know it's just a TV show. Really, I know that.