If I'm CC, I worry about what effect that will have on my arm. I'm sure his agent and potential suitors are concerned.
This is also a concern for the Mets as well. I'm not sure if it's worth endangering his arm since this team is unlikely to the Series with the bullpen. There's also similar concern over Pelfrey. There apparently is some rule, which has been borne out, that if you're a young pitcher and you pitch more than thirty innings from your prior year, injury almost always results, which is why teams always exercise caution with young pitchers.
Let's face it, the Cubs are the most likely team to get to the Series for the Mets and Brewers, this is probably more about saving face: the Mets, because it wouldn't be good if this happened two years in a row; and the Brewers, same reason.
I'm pretty sure the Cubs would rather play the Mets in the first round because they can't play the Brewers, which would leave them facing the Phillies, a stronger team than the Mets (the key difference between the two being a better bullpen).