There seems to be not many effective DPA attacks against SHA
How do you come to that conclusion? Is it because there aren't many published results of using DPA attacks against SHA? Well, that's mostly because SHA is most often used to hash publicly available data, and so there's less of a point using a DPA attack to recover that data.
Now, any side channel attack (such as DPA) is actually an attack against the implementation, not against the base crypto. Of course, if we consider DPA attacks against SHA implementations, we need to consider "how difficult is it to make a SHA implementation that is strong against DPA attacks?"
Well, there's nothing in the SHA architecture (either SHA-1, SHA-2 or SHA-3) that makes it specifically easy to provide such protection. Now, you could create such an implementation (using, say, thresholding to disguise the individual bits); however that's likely to be significantly slower than a standard implementation.