The problem with anonymizing the samples completely is that it makes it impossible to add new information about the donors' health since birth, which would make the samples much more useful for researchers. Totally anonymous samples could be used, for example, to look at gene frequencies, but not a lot more. The greatest value to researchers would be if they could associate the samples with subsequent health information so that they could look for genetic markers associated with specific diseases. That can only happen if it's possible to connect the samples to their donors' health records.
The ideal approach would be to have a completely trustworthy organization hold the samples, associate them with the health records, and then anonymize the samples before providing them to researchers. That would let you have the benefits of the research without the drawbacks of destroying people's privacy. The question is whether we trust our government to do that.