well in many countries this privacy has been revoked by law, and father records are still kept if the child want to know his/her biological father. since then many people stopped donating sperms.
on the topic, I guess a new technique with stem cells will remove the need of sperm donor, a healthy sperms can be grown from the mothers stem cells. I guess that will be more acceptable as there will be no need of donated sperms or eggs in that scenario. on the wrong side, there will be no need of men any more!!!
in most islamic school of thoughts, donation of any organ without the requirement of life saving or research is not allowed as human body should be protected.
and in child birth, child has to be biological child of the father and mother. good option is adoption. I know a very nice and very well off couple from my friends, they are and have been trying so long, they have adopted 2 cute girls, one is orphan from last earthquake. mashallah they all are happy family.