First off, no one knows for sure that he will miss half a season, or even any time for that matter. Chances are that he will miss some time based on history, so you prepare for that, but it's not a given. Since 2010, his GS/IP have been 28/173.2, 14/82.2, 29/189.1, 16/108.1, 28/170.1, 18/113.1. Three out of the 6 years he has made close to 30 starts, or has given the team close to a full season.
Yes, I realize that that is not exactly a strong track record, but he will also not necessarily last only 1/2 a season. The $13 mil is worth the risk.
As far as the back up plan goes, for one, I would not rely on Clay to be the team's ace, so that if/when he does go down, we will not be losing our best pitcher. I realize that his replacement is likely going to be a downgrade if Clay is pitching well to that point. However, that is not necessarily the case either. There is the possibility that one of the young arms can fill in admirably. There is also the possibility of an in-season trade, depending on the timing of the potential injury.
Picking up Clay's option is a good start to building the rotation for next year. I don't see it as an excuse to stink again.