He's specifically concerned with "care ethics" and makes the argument that markets extend our care much farther afield than the kith and kin that we are naturally inclined to care for. I think there is an important limit to this argument in that markets can only (1.) produce results that might be comparable to what we like about the results from the intent to care for others and (2.) reduce overt hostility or suspicion of others that is obviously not compatible with care. In other words, when Kevin (in introducing care ethics) makes the distinction between care ethicists who consider intent critical and those who consider results critical, I think markets can ultimately only satisfy the latter. And maybe that's fine - if that's what we can accomplish with markets then that's still a good thing. He even raises this point parenthetically in his post so although I wrote this paragraph up before even coming to that point in his post, he seems to be thinking along the same lines.
Kevin further argues, though, that markets create the opportunity for caring relationships to emerge that wouldn't have emerged otherwise. This is very likely true. We make friends at work. We get to know store owners, etc. This is exactly why I think the "buy local" movement is not as problematic as a lot of people treat it. There is a different social content between buying local and buying from extent networks of trade. Obviously I acknowledge the benefits of globalization but I'll never have the opportunity to form social bonds with the people that sew my clothes an ocean away in the same way I can form those bonds with local store owners. Unless you're a misanthrope, those bonds matter.
I'll add one last thought from the perspective of gender economics (which works a lot with the economics of care). One of the things gender economists point out is that care is one of those "goods" whose very nature changes when it's exchanged in a market setting. If I sent you a bill for coming to visit you in the hospital when you were sick you wouldn't feel particularly cared for anymore. To some extent market substitutes are substitutable, but they're not perfect substitutes. This raises issues around the preferences of the caregiver and whether those are sufficient to really provide the sort of care we require to be fully functional human beings.