The Empire hadn't sentenced MUKirk to death. It was MUSulu that did that, and look how that turned out. MUSulu may have sent word to the Empire as to why he was acting, but once MUKirk was back, and with MUSulu having spent some time in the booth for insubordination, the Empire would have been dealing with MUKirk, with all that entails.
So MUSpock now has a choice. He can do nothing, and nothing changes, or he can come up with a plan for changing the future. What we saw in DS9 was one version where he came up with the wrong solution, one that saw a violent end to the Empire, and the subjugation of its member races.