Because they’ve already entered into treaties making the offenses involved matters of universal jutisdiction which any state can prosecute their citizens for, and as a State Party to the Rome Statute, they would have more influence over the fairness and process of the ICC than they would over any national system outside of their own.

Also, because they are tired of the diplomatic cost and expense of working with other countries to set up ad hoc tribunals for particular conflicts and want to get the job done once and properly. (That's actually why the US was one of the leaders of the effort that produced the ICC, even though it did a U-turn against it at the last minute.)