Sperm donation is easy, um, mechanically. As the donors say, they get paid to do something they do for free anyway. And the sperm donor business is so successful that there are for-profit companies, as well as many labs and non-profits. The technological and economic aspects get better and easier every day.
What is getting harder is to stay anonymous. The Donor Sibling Registry brings together children of the same father to compare characteristics. The biographical facts that donors give about themselves are becoming easier to search and cross list. And if the donor is ever in a DNA registry, each of his children is full of enough comparable genetic information to establish a match. Sperm banks are starting to back off of their claim of permanent anonymity. They promise that the bank will not release the donor's identity, but admit that technological advances may make them findable anyway.
I think the other part of anonymous sperm donation that is getting harder is the belief that children made from your sperm are not, in a deep way, related to you. Of course donors know that they are the fathers of the children made with their sperm. I think they have underestimated how strong a tie that actually makes, even if they never meet their children. For several generations social science has convinced the educated public that nurture trumps nature. As a card-carrying sociologist I was trained in this view. I have changed my mind over years of study and parenthood. I am holding the line at 50/50 in the nature/nurture debate.
I think there are so many points of biological similarity between fathers and their children that it would be an unusual man, and a very unusual child, who would not be moved by the similarity. Moved to try to make a personal connection. Which would make anonymously donating sperm and walking away forever harder to do.