Kyle Shanahan wanted a third OT possession; the Chiefs didn't plan on letting one happen.
www.nbcsports.com
This thinking by SF is a perfect illustration of overthinking football strategy by these “brilliant” coaches. SF takes the ball first so that they have the first chance with the ball during sudden death. Having the ball first during sudden death is a huge advantage, so this strategy makes perfect sense to the analytics nerds.
The problem is that you have a very low chance of the game ever getting to sudden death. As pointed out in the article, KC was going for 2 if they got a TD after a SF TD. So the only way that game goes to sudden death is if neither team scores on its first possession, or if both teams score a FG on their first possession.
Meanwhile, getting the ball second at the beginning of a two-possession OT is its own huge advantage, with the team going on defense first having a 100% chance of having that advantage.
But SF overthought the situation, as is commonly done in the age of analytics.