To a politician, brokering peace is almost as orgasmic a prospect as is declaring war.
Hemmed and harried by the humdrum of domestic politics, it is irresistible. The international stage may provide only a brief window to strut their stuff, but the exposure is golden and the potential benefits usually outweigh the risks.
No one honestly expects you to succeed, especially not with the big, gnarly, knotty wars, so it doesn’t much matter if you fail. At least you tried, you